o
    *ήc<                    @   s\  d dl Z d dlmZ d dlmZ d dlmZ d dlmZ d dl	m
Z
 d dlmZmZ d dlmZ d d	lmZ d d
lmZ d dlmZ d dlmZ d dlmZmZmZ d dlmZmZ d dlm Z  d dl!m"Z" d dl#m$Z$ d dl%m&Z&m'Z' d dl(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3 e/Z4e2Z5G dd deZ6ee6dd Z7dd Z8e8Z9dd Z:dS )    N)S)Add)Tuple)FunctionMul)NumberRational)Pow)default_sort_keySymbol)SympifyError)requires_partial)
PRECEDENCE
precedenceprecedence_traditional)Printerprint_function)sstr)has_variety)sympy_deprecation_warning)
prettyForm
stringPict)hobjvobjxobjxsympretty_symbolpretty_atompretty_use_unicodegreek_unicodeUpretty_try_use_unicode	annotatedc                   @   s	  e Zd ZdZdZddddddddddd
Zdd	d
Zdd Zedd Z	dd Z
dd Zdd Zdd ZdddZeZdd Zdd Zdd Zd d! Zd"d# Zd$d% Zd&d' Zd(d) Zd*d+ ZeZeZeZeZeZeZeZeZ eZ!d,d- Z"d.d/ Z#d0d1 Z$d2d3 Z%d4d5 Z&d6d7 Z'd8d9 Z(dd:d;Z)d<d= Z*d>d? Z+d@dA Z,dBdC Z-dDdE Z.ddFdGZ/ddHdIZ0dJdK Z1dLdM Z2dNdO Z3dPdQ Z4dRdS Z5dTdU Z6dVdW Z7dXdY Z8dZd[ Z9d\d] Z:d^d_ Z;d`da Z<dbdc Z=ddfdgZ>dhdi Z?djdk Z@dldm ZAdndo ZBdpdq ZCdrds ZDdtdu ZEdvdw ZFdxdy ZGdzd{ ZHd|d} ZId~d ZJdd ZKdd ZLdd ZMdd ZNdd ZOdd ZPdd ZQdd ZRdd ZSdd ZTdd ZUdd ZVdd ZWdd ZXdd ZYdd ZZdd Z[dd Z\i fddZ]dd Z^dd Z_dd Z`dd Zadd Zbdd Zcdd Zddd Zedd ZfdddZgdd Zhdd Zidd Zjdd Zk		ĐdddƄZlddȄ Zmddʄ Zndd̄ Zodd΄ Zp			ĐdddфZqddӄ ZreddՄ Zsddׄ Ztddل Zuddۄ Zvdd݄ Zwdd߄ Zxdd Zydd Zzdd Z{dd Z|dd Z}dd Z~dd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d Zdd Zdd Zdd Zdd	 Zd
d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZdܐddZd d! Zd"d# Zd$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Zd4d5 Zd6d7 Zd8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM ZdNdO ZeZeZeZdddϐdPdQ dfdRdSZdTdU ZdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Zd`da Zdbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo Zdpdq ZÐdrds ZĐdtdu ZŐdvdw ZƐdxdy Zǐdzd{ ZȐd|d} Zɐd~d Zʐdd Zːdd Z̐dd Z͐dd Zΐdd Zϐdd ZАdd Zѐdd ZҐdd ZeZԐdd ZՐdd Z֐dd Zאdd Zؐdd Zِdd Zڐdd Zېdd Zܐdd Zݐdd Zސdd Zߐdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZddÄ ZdĐdń ZdƐdǄ ZdȐdɄ Zdʐd˄ Zd̐d̈́ Zdΐdτ ZdАdф ZdҐdӄ ZdԐdՄ Zd֐dׄ Zdؐdل Zdڐdۄ ZdS (  PrettyPrinterz?Printer, which converts an expression into 2D ASCII-art figure._prettyNautoTplaini)
order	full_precuse_unicode	wrap_linenum_columnsuse_unicode_sqrt_charroot_notationmat_symbol_styleimaginary_unitperm_cyclicc                 C   sV   t | | t| jd tstd| jd | jd dvr)td| jd d S )Nr2   z&'imaginary_unit' must a string, not {})r)   jz4'imaginary_unit' must be either 'i' or 'j', not '{}')r   __init__
isinstance	_settingsstr	TypeErrorformat
ValueError)selfsettings r>   C/tmp/pip-target-vg8gfxp4/lib/python/sympy/printing/pretty/pretty.pyr5   /   s   zPrettyPrinter.__init__c                 C      t t|S Nr   r8   r<   exprr>   r>   r?   emptyPrinter7      zPrettyPrinter.emptyPrinterc                 C   s   | j d rdS t S )Nr,   T)r7   r    r<   r>   r>   r?   _use_unicode:   s   
zPrettyPrinter._use_unicodec                 C   s   |  |jdi | jS )Nr>   )_printrenderr7   rC   r>   r>   r?   doprintA      zPrettyPrinter.doprintc                 C   s   |S rA   r>   r<   er>   r>   r?   _print_stringPictE   s   zPrettyPrinter._print_stringPictc                 C   s   t |S rA   )r   rM   r>   r>   r?   _print_basestringH   s   zPrettyPrinter._print_basestringc                 C   s&   t | |j  }t |d }|S )Natan2)r   
_print_seqargsparensleftr<   rN   pformr>   r>   r?   _print_atan2K   s   zPrettyPrinter._print_atan2Fc                 C   s   t |j|}t|S rA   )r   namer   )r<   rN   	bold_namesymbr>   r>   r?   _print_SymbolP   s   zPrettyPrinter._print_Symbolc                 C   s   |  || jd dkS )Nr1   bold)r\   r7   rM   r>   r>   r?   _print_MatrixSymbolT   s   z!PrettyPrinter._print_MatrixSymbolc                 C   s,   | j d }|dkr| jdk}tt||dS )Nr+   r'      )r+   )r7   _print_levelr   r   )r<   rN   r+   r>   r>   r?   _print_FloatW   s   

zPrettyPrinter._print_Floatc                 C   ~   |j }|j}| |}t|d }t|d }t|| td }t|d }t|| | }t|d }|S )N()MULTIPLICATION SIGN_expr1_expr2rI   r   rU   rightr"   r<   rN   vec1vec2rW   r>   r>   r?   _print_Cross_      
zPrettyPrinter._print_Crossc                 C   `   |j }| |}t|d }t|d }t|| td }t|| td }|S )Nrc   rd   re   NABLA_exprrI   r   rU   ri   r"   r<   rN   vecrW   r>   r>   r?   _print_Curlk      
zPrettyPrinter._print_Curlc                 C   ro   )Nrc   rd   DOT OPERATORrp   rq   rs   r>   r>   r?   _print_Divergencet   rv   zPrettyPrinter._print_Divergencec                 C   rb   )Nrc   rd   rw   rf   rj   r>   r>   r?   
_print_Dot}   rn   zPrettyPrinter._print_Dotc                 C   H   |j }| |}t|d }t|d }t|| td }|S )Nrc   rd   rp   rq   r<   rN   funcrW   r>   r>   r?   _print_Gradient      
zPrettyPrinter._print_Gradientc                 C   rz   )Nrc   rd   	INCREMENTrq   r{   r>   r>   r?   _print_Laplacian   r~   zPrettyPrinter._print_Laplacianc                 C   s4   zt t|jj| dW S  ty   | | Y S w )N)printer)r   r   	__class____name__KeyErrorrE   rM   r>   r>   r?   _print_Atom   s
   zPrettyPrinter._print_Atomc                 C   s&   | j r| |S ddg}| |ddS )Nz-oooorc   rd   )rH   r   rR   )r<   rN   inf_listr>   r>   r?   _print_Reals   s   
zPrettyPrinter._print_Realsc                 C   D   |j d }| |}|jr|js|jst|  }t|d }|S Nr   !)rS   rI   
is_Integeris_nonnegative	is_Symbolr   rT   rU   r<   rN   xrW   r>   r>   r?   _print_subfactorial      

z!PrettyPrinter._print_subfactorialc                 C   r   r   rS   rI   r   r   r   r   rT   ri   r   r>   r>   r?   _print_factorial   r   zPrettyPrinter._print_factorialc                 C   r   )Nr   z!!r   r   r>   r>   r?   _print_factorial2   r   zPrettyPrinter._print_factorial2c                 C   st   |j \}}| |}| |}dt| |  }t|| }t|| }t|dd }|jd d |_|S )N rc   rd   r_      )rS   rI   maxwidthr   aboverT   baseline)r<   rN   nkn_pformk_pformbarrW   r>   r>   r?   _print_binomial   s   


zPrettyPrinter._print_binomialc                 C   sL   t dt|j d }| |j}| |j}t t|||dt ji}|S )Nr   binding)	r   r   rel_oprI   lhsrhsr   nextOPENr<   rN   oplrrW   r>   r>   r?   _print_Relational   s
   zPrettyPrinter._print_Relationalc                 C   s   ddl m}m} | jr@|jd }| |}t||r!| j|ddS t||r-| j|ddS |j	r9|j
s9t|  }t|d S | |S )Nr   )
EquivalentImpliesu   ⇎)altcharu   ↛   ¬)sympy.logic.boolalgr   r   rH   rS   rI   r6   _print_Equivalent_print_Implies
is_Booleanis_Notr   rT   rU   _print_Function)r<   rN   r   r   argrW   r>   r>   r?   
_print_Not   s   




zPrettyPrinter._print_Notc                 C   s   |j }|rt|j td}|d }| |}|jr!|js!t|  }|dd  D ]#}| |}|jr:|js:t|  }t|d|  }t|| }q'|S )Nkeyr   r_    %s )	rS   sortedr   rI   r   r   r   rT   ri   )r<   rN   charsortrS   r   rW   	pform_argr>   r>   r?   __print_Boolean   s   

zPrettyPrinter.__print_Booleanc                 C       | j r	| |dS | j|ddS )N   ∧Tr   rH   _PrettyPrinter__print_Booleanr   rM   r>   r>   r?   
_print_And     zPrettyPrinter._print_Andc                 C   r   )Nu   ∨Tr   r   rM   r>   r>   r?   	_print_Or  r   zPrettyPrinter._print_Orc                 C   r   )Nu   ⊻Tr   r   rM   r>   r>   r?   
_print_Xor  r   zPrettyPrinter._print_Xorc                 C   r   )Nu   ⊼Tr   r   rM   r>   r>   r?   _print_Nand  r   zPrettyPrinter._print_Nandc                 C   r   )Nu   ⊽Tr   r   rM   r>   r>   r?   
_print_Nor$  r   zPrettyPrinter._print_Norc                 C   s$   | j r| j||p	dddS | |S )Nu   →Fr   r   r<   rN   r   r>   r>   r?   r   *  s   
zPrettyPrinter._print_Impliesc                 C   s$   | j r| ||p	dS | j|ddS )Nu   ⇔Tr   r   r   r>   r>   r?   r   0  s   zPrettyPrinter._print_Equivalentc                 C   s(   |  |jd }t|td|  S )Nr   _)rI   rS   r   r   r   r   rV   r>   r>   r?   _print_conjugate6  s   zPrettyPrinter._print_conjugatec                 C   s$   |  |jd }t|dd }|S )Nr   |)rI   rS   r   rT   rV   r>   r>   r?   
_print_Abs:  s   zPrettyPrinter._print_Absc                 C   4   | j r| |jd }t|dd }|S | |S )Nr   lfloorrfloorrH   rI   rS   r   rT   r   rV   r>   r>   r?   _print_floor?  
   
zPrettyPrinter._print_floorc                 C   r   )Nr   lceilrceilr   rV   r>   r>   r?   _print_ceilingG  r   zPrettyPrinter._print_ceilingc                 C   s  t |jr| jrtd}nd}d }d}t|jD ]8\}}| |}t|| }||7 }|j	r3|dkr;|tt
| }|d u rB|}qt|d }t|| }qt| |j dtji}	t|}
|dkdkrq|
tt
| }
t|
tj| }
|
jd |
_tt|
|	 }
tj|
_|
S )NPARTIAL DIFFERENTIALdr   r_   r   r   F)r   rD   rH   r"   reversedvariable_countrI   r   rU   r   r8   ri   rT   FUNCbelowr   LINEr   r   MULr   )r<   derivderiv_symbolr   count_total_derivsymnumsdsfrW   r>   r>   r?   _print_DerivativeO  s8   

zPrettyPrinter._print_Derivativec                 C   s   ddl m}m} || krtd}t|  S || j}|g kr0| |j	d }t|  S td}|D ]}| t
t|dd}t|| }q6|S )Nr   PermutationCycle r_   ,) sympy.combinatorics.permutationsr   r   r   r   rT   listcyclic_formrI   sizer8   tuplereplaceri   )r<   dcr   r   cycdc_listr)   r   r>   r>   r?   _print_Cyclet  s   
zPrettyPrinter._print_Cyclec                 C   s   ddl m}m} |j}|d urtd| ddddd n| jd	d
}|r,| ||S |j}t	t
t|}td}d
}t||D ](\}	}
| |	}| |
}t|| }|r\d}nt|d }t|| }qBt|  S )Nr   r   zw
                Setting Permutation.print_cyclic is deprecated. Instead use
                init_printing(perm_cyclic=z).
                z1.6z#deprecated-permutation-print_cyclic   )deprecated_since_versionactive_deprecations_target
stacklevelr3   Tr   Fr   )r   r   r   print_cyclicr   r7   getr   
array_formr   rangelenr   ziprI   r   r   rU   ri   rT   )r<   rD   r   r   r3   lowerupperresultfirstur   s1s2colr>   r>   r?   _print_Permutation  s6   


z PrettyPrinter._print_Permutationc                 C   s  |j }| |}|jrt|  }|}|jD ]}| |d }| dkr+t|  }t|d| }qd}d }|jD ]}	| }
|
d }| j	 }|rO|d7 }t
d|}t|}|j||
 d  |_t|	dkrt|	dkrytd}| |	d }t|	dkr| |	d }| |	d }|rtdd|  }t|d	|  }tdd
|  }t|d	|  }t|| }t|| }|st|d	 }|r|}d}q;t|| }q;t|| }tj|_|S )Nr   r_   z dTr   intr      r      F)functionrI   is_Addr   rT   limitsr   ri   heightrH   r   r   r  r   rU   r   r   r   r   )r<   integralr   prettyFr   r   	prettyArg	firsttermr   limhH
ascii_modevintrW   prettyAprettyBspcr>   r>   r?   _print_Integral  s\   



zPrettyPrinter._print_Integralc                 C   s  |j }| |}tdd}tdd}tdd}| jr!tdd}d}| }d}d}	d}
|jD ]}| |\}}|d d	 d
 d }|| ||d   | | g}t|d D ]}|d| d|d   | d  qVt	d}t
|j|  }t|	| }	|r| }
t
|| }t
|| }|rd|_d}| }t	d}t
|jdg|d    }t
|| }t
|| }q.|	|
d  |_t
j|_|S )Nr   r_   r   -u   ┬Tr   r      r  r   r   F)termrI   r   rH   r  r  '_PrettyPrinter__print_SumProduct_Limitsr  appendr   r   stackr   r   r   r   ri   r   r   )r<   rD   r|   pretty_funchorizontal_chr
corner_chrvertical_chrfunc_heightr  	max_uppersign_heightr  pretty_lowerpretty_upperr   
sign_linesr   pretty_signr  paddingr>   r>   r?   _print_Product  sH   





$zPrettyPrinter._print_Productc                    s4    fdd}  |d }||d |d }||fS )Nc                    s>   t dtd d } | } |}t t||| }|S )Nr   ==)r   r   rI   r   r   )r   r   r   r   r   rW   rG   r>   r?   print_start.  s
   

z<PrettyPrinter.__print_SumProduct_Limits.<locals>.print_startr   r   r_   rI   )r<   r  r5  prettyUpperprettyLowerr>   rG   r?   __print_SumProduct_Limits-  s   z'PrettyPrinter.__print_SumProduct_Limitsc                 C   sX  | j  }dd }|j}| |}|jrt|  }| d }d}d}d}	|jD ]n}
| |
\}}t	|| }|||
 |
 |\}}}}td}t|j|  }|rX| }	t|| }t|| }|rz| j|| d |j  8  _d}td}t|jdg|   }t|| }t|| }q(|s|nd}||	d  | |_tj|_|S )	Nc              	   S   s  ddd}t | d}|d }|d }| d }g }	|r|	d| d  |	dd|d    td|D ]}
|	d	d|
 d||
  f  q3|rV|	d
d| d||  f  ttd|D ]}
|	dd|
 d||
  f  q]|	dd|d   d  ||| |	|fS || }|| }tdd}|	d|  td|D ]}
|	dd|
 |d d||
 d  f  qttd|D ]}
|	dd|
 |d d||
 d  f  q|	|d |  ||d|  |	|fS )N<^>c                 S   s|   |rt | |kr
| S |t |  }|dv s|tdvr | d|  S |d }d| }|dkr2d| |  S ||  d|t |   S )N)r:  <r:  r   r   >)r  r   )r   widhowneedhalfleadr>   r>   r?   adjust=  s   z6PrettyPrinter._print_Sum.<locals>.asum.<locals>.adjustr   r_   r   r   z\%s`z%s\%sz%s)%sz%s/%s/r   sumr  r   z%s%s%s   )Nr:  )r   r%  r  r   r   )	hrequiredr  r  	use_asciirB  r  r   wmorelinesr)   vsumr>   r>   r?   asum<  s6   

  
**z&PrettyPrinter._print_Sum.<locals>.asumr   Tr   r   Fr   )rH   r  rI   r  r   rT   r  r  r$  r   r   r   r&  r   r   r   ri   r   r   )r<   rD   r  rL  r   r  r  r  r,  r-  r  r8  r7  r   r  slines
adjustment
prettySignpadascii_adjustmentr>   r>   r?   
_print_Sum9  sF   *


zPrettyPrinter._print_Sumc           	      C   s   |j \}}}}| |}t|td krt|dd }td}| |}| jr0t|d }nt|d }t|| | }t|dksO|t	j
t	jfv rRd}n| jr_t|d	kr]d
nd}t|| | }t|| }t||dtji}|S )Nr   rc   rd   r  u   ─→z->z+-r   +u   ⁺u   ⁻r   )rS   rI   r   r   r   rT   rH   ri   r8   r   InfinityNegativeInfinityr   r   )	r<   r   rN   zz0dirELimLimArgr>   r>   r?   _print_Limit  s$   

zPrettyPrinter._print_Limitc                    s  |}i  t |jD ]}t |jD ]| ||f  |f< qq	d}d}dg|j }t |jD ]t fddt |jD pBdg|< q0d}t |jD ]q}d}t |jD ]K |f }	|	 | ksiJ | |	  }
|
d }|
| }t|	d|  }	t|	d|  }	|du r|	}qWt|d|  }t||	 }qW|du r|}qNt |D ]	}t|	d }qt|	| }qN|du rtd	}|S )
zL
        This method factors out what is essentially grid printing.
        r   r_   c                       g | ]
} |f   qS r>   r   .0r)   Msr4   r>   r?   
<listcomp>      z8PrettyPrinter._print_matrix_contents.<locals>.<listcomp>r   Nr   r   )
r  rowscolsrI   r   r   r   ri   rU   r   )r<   rN   Mr)   hsepvsepmaxwDD_rowr   wdeltawleftwrightr   r>   rb  r?   _print_matrix_contents  sH   *z$PrettyPrinter._print_matrix_contents[]c                 C   s,   |  |}| d |_t||| }|S )Nr   )rq  r  r   r   rT   )r<   rN   lparensrparensrl  r>   r>   r?   _print_MatrixBase  s   
zPrettyPrinter._print_MatrixBasec                 C   sl   |j }|jr.ddlm} t||r| j|jdddS | |}| d |_	t
|dd S | j|dddS )Nr   )BlockMatrixr   )rt  ru  r   )r   is_MatrixExpr&sympy.matrices.expressions.blockmatrixrw  r6   rv  blocksrI   r  r   r   rT   )r<   rN   matrw  rl  r>   r>   r?   _print_Determinant  s   

z PrettyPrinter._print_Determinantc                 C   *   | j rd}nd}| j|jd d |dd dS )Nu   ⊗.*c                 S      t | td kS Nr   r   r   r   r>   r>   r?   <lambda>      z4PrettyPrinter._print_TensorProduct.<locals>.<lambda>parenthesizerH   rR   rS   )r<   rD   circled_timesr>   r>   r?   _print_TensorProduct     z"PrettyPrinter._print_TensorProductc                 C   r}  )Nr   z/\c                 S   r  r  r  r  r>   r>   r?   r    r  z3PrettyPrinter._print_WedgeProduct.<locals>.<lambda>r  r  )r<   rD   wedge_symbolr>   r>   r?   _print_WedgeProduct  r  z!PrettyPrinter._print_WedgeProductc                 C   s<   |  |j}t|dd }| d |_t|d }|S )Nrc   rd   r   tr)rI   r   r   rT   r  r   rU   )r<   rN   rl  r>   r>   r?   _print_Trace  s
   zPrettyPrinter._print_Tracec                 C   s   ddl m} t|j|r%|jjr%|jjr%| t|jj	d|j|jf  S | |j}t
|  }| j|j|jfddjdddd }t
t||d	t
ji}||_||_|S )
Nr   MatrixSymbolz_%d%d, 	delimiterrr  rs  rU   ri   r   )sympy.matricesr  r6   parentr)   	is_numberr4   rI   r   rY   r   rT   rR   r   r   r   
prettyFunc
prettyArgs)r<   rD   r  r  prettyIndicesrW   r>   r>   r?   _print_MatrixElement'  s,   
z"PrettyPrinter._print_MatrixElementc                    s   ddl m}  |j}t|j|st|  } fdd} j||j|jj	||j
|jjfddjddd	d }tt||d
tji}||_||_|S )Nr   r  c                    sT   t | } | d dkr| d= | d dkrd| d< | d |kr!d| d< t j| dd S )Nr   r_   r   r   :r  )r   r   rR   )r   dimrG   r>   r?   ppsliceB  s   z1PrettyPrinter._print_MatrixSlice.<locals>.ppslicer  r  rr  rs  r  r   )r  r  rI   r  r6   r   rT   rR   rowslicerf  colslicerg  r   r   r   r  r  )r<   mr  r  r  r  rW   r>   rG   r?   _print_MatrixSlice<  s,   	
z PrettyPrinter._print_MatrixSlicec                 C   sV   |j }| |}ddlm}m} t||s#t||s#|jr#t|  }|td }|S )Nr   r  rw  T)	r   rI   r  r  rw  r6   rx  r   rT   )r<   rD   r{  rW   r  rw  r>   r>   r?   _print_TransposeW  s   

zPrettyPrinter._print_Transposec                 C   sj   |j }| |}| jrtd}ntd}ddlm}m} t||s/t||s/|jr/t|	  }|| }|S )Nu   †rS  r   r  )
r   rI   rH   r   r  r  rw  r6   rx  rT   )r<   rD   r{  rW   dagr  rw  r>   r>   r?   _print_Adjointa  s   


zPrettyPrinter._print_Adjointc                 C   s(   |j jdkr| |j d S | |j S )Nr_   r_   r   r   )rz  shaperI   )r<   Br>   r>   r?   _print_BlockMatrixo  s   z PrettyPrinter._print_BlockMatrixc                 C   s   d }|j D ]8}| |}|d u r|}q| d }t| r-tt|d }| |}ntt|d }tt|| }q|S )Nr   r    + )rS   rI   as_coeff_mmulr   could_extract_minus_signr   r   r   )r<   rD   r   itemrW   coeffr>   r>   r?   _print_MatAddt  s   

zPrettyPrinter._print_MatAddc                 C   s   t |j}ddlm} ddlm} ddlm} t|D ]'\}}t	|t
|||fr;t|jdkr;t| |  ||< q| |||< qtj| S )Nr   HadamardProduct)KroneckerProductMatAddr_   )r   rS   #sympy.matrices.expressions.hadamardr  $sympy.matrices.expressions.kroneckerr  !sympy.matrices.expressions.mataddr  	enumerater6   r   r  r   rI   rT   __mul__)r<   rD   rS   r  r  r  r)   ar>   r>   r?   _print_MatMul  s   

zPrettyPrinter._print_MatMulc                 C      | j rtdS tdS )Nu   𝕀IrH   r   rC   r>   r>   r?   _print_Identity     zPrettyPrinter._print_Identityc                 C   r  )Nu   𝟘0r  rC   r>   r>   r?   _print_ZeroMatrix  r  zPrettyPrinter._print_ZeroMatrixc                 C   r  )Nu   𝟙1r  rC   r>   r>   r?   _print_OneMatrix  r  zPrettyPrinter._print_OneMatrixc                 C   s4   t |j}t|D ]\}}| |||< q	tj| S rA   )r   rS   r  rI   r   r  r<   rD   rS   r)   r  r>   r>   r?   _print_DotProduct  s   

zPrettyPrinter._print_DotProductc                 C   sL   |  |j}ddlm} t|j|s|jjrt|  }||  |j }|S )Nr   r  )	rI   baser  r  r6   rx  r   rT   exp)r<   rD   rW   r  r>   r>   r?   _print_MatPow  s   zPrettyPrinter._print_MatPowc                    sZ   ddl m  ddlm ddlm | jrtd}nd}| j|j	d d | fddd	S )
Nr   r  r  MatMulRingr~  c                    s   t |  fS rA   r6   r  r  r  r  r>   r?   r    r  z6PrettyPrinter._print_HadamardProduct.<locals>.<lambda>r  )
r  r  r  r  !sympy.matrices.expressions.matmulr  rH   r   rR   rS   r<   rD   delimr>   r  r?   _print_HadamardProduct  s   
z$PrettyPrinter._print_HadamardProductc                 C   sp   | j rtd}n| d}| |j}| |j}t|jtd k r(t|  }tt	
||dtji}|| S )Nr  .r   r   )rH   r   rI   r  r  r   r   r   rT   r   r   r   )r<   rD   circpretty_base
pretty_exppretty_circ_expr>   r>   r?   _print_HadamardPower  s   


z"PrettyPrinter._print_HadamardPowerc                    sH   ddl m  ddlm | jrd}nd}| j|jd d | fdddS )	Nr   r  r  u    ⨂ z x c                    s   t |  fS rA   r  r  r  r  r>   r?   r    s    z7PrettyPrinter._print_KroneckerProduct.<locals>.<lambda>r  )r  r  r  r  rH   rR   rS   r  r>   r  r?   _print_KroneckerProduct  s   z%PrettyPrinter._print_KroneckerProductc                 C   s"   |  |jj}t|dd }|S Nrr  rs  )rI   lamdarD   r   rT   )r<   Xrl  r>   r>   r?   _print_FunctionMatrix  s   z#PrettyPrinter._print_FunctionMatrixc                 C   sP   |j dks|j |j}}t|t|ddddd}| |S | d| |j S )Nr_   r]  Fevaluate)r   denr   r
   
_print_MulrI   )r<   rD   r   r  resr>   r>   r?   _print_TransferFunction  s
   

z%PrettyPrinter._print_TransferFunctionc                 C   s>   t |j}t|jD ]\}}t| |  ||< q
tj| S rA   )r   rS   r  r   rI   rT   r  r  r>   r>   r?   _print_Series  s   

zPrettyPrinter._print_Seriesc                 C   s   ddl m} t|j}g }tt|D ]7\}}t||r9t|jdkr9| |}|	 d |_
|t|   q| |}|	 d |_
|| qtj| S )Nr   )MIMOParallelr_   r   )sympy.physics.control.ltir  r   rS   r  r   r6   r  rI   r  r   r%  r   rT   r  )r<   rD   r  rS   pretty_argsr)   r  
expressionr>   r>   r?   _print_MIMOSeries  s   



zPrettyPrinter._print_MIMOSeriesc                 C   sh   d }|j D ],}| |}|d u r|}qtt| }| d |_tt|d }tt|| }q|S )Nr   r  )rS   rI   r   r   r   r  r   )r<   rD   r   r  rW   r>   r>   r?   _print_Parallel  s   

zPrettyPrinter._print_Parallelc                 C   s   ddl m} d }|jD ]8}| |}|d u r|}qtt| }| d |_tt|d }t	||r;| d |_tt|| }q|S )Nr   )TransferFunctionMatrixr   r  r_   )
r  r  rS   rI   r   r   r   r  r   r6   )r<   rD   r  r   r  rW   r>   r>   r?   _print_MIMOParallel  s   


z!PrettyPrinter._print_MIMOParallelc           
      C   s  ddl m}m} |j|dd|j}}t||rt|jn|g}t|j|r,t|jjn|jg}t||rEt|j|rE|g ||R  }nYt||ret|j|re|j|krZ|| }nD|g ||jR  }n9t||rt|j|r||kry|| }n%||g|R  }n||kr|| }n|j|kr|| }n	|g ||R  }t	t
| | }	|	 d |	_|jdkrt	t
|	d nt	t
|	d }	t	t
|	| | }	| ||	 S )Nr   )TransferFunctionSeriesr_   r   r]  r   - )sympy.physics.controlr  r  sys1varr6   r   rS   sys2r   r   r   rI   r  r   sign)
r<   rD   r  r  r   tfnum_arg_listden_arg_listr  denomr>   r>   r?   _print_Feedback  s:   






zPrettyPrinter._print_Feedbackc                 C   s   ddl m}m} | ||j|j}| |j}tt| }|j	dkr,tt
d| ntt
d| }tt| }d|_tt
|d }| d |_t|td}t|j|rb| d	 |_tt|| }|S )
Nr   )
MIMOSeriesr  r]  zI + zI - z-1 r   r   r_   )r  r  r  rI   r  r  r   r   r   r  ri   rT   r   r  r  r6   )r<   rD   r  r  inv_matplant	_feedbackr>   r>   r?   _print_MIMOFeedback=  s    z!PrettyPrinter._print_MIMOFeedbackc                 C   s>   |  |j}| d |_| jrtd nd}t|| }|S )Nr_   tauz{t})rI   	_expr_matr  r   rH   r!   r   ri   )r<   rD   r{  	subscriptr>   r>   r?   _print_TransferFunctionMatrixO  s
   z+PrettyPrinter._print_TransferFunctionMatrixc                 C   s  ddl m} | jstd||jkrt|jjS g }g }t||r(| 	 }nd|fg}|D ]M\}}t
|j	 }|jdd d |D ]7\}	}
|
dkrU|d|	j  n |
d	krb|d
|	j  n| |
 d }||d |	j  ||	j qDq/|d dr|d dd  |d< n|d dr|d dd  |d< g }dg}g }t|D ]}\}}|d d|v r(|}||| d}d|v rtt|D ],}d||< || dkr||d  dkr|d | d d ||  ||d d   } nqn)d|v r$|d}|d	kr$d||< |d | d d ||  ||d d   }|||< qdd |D }tdd |D }d|v r_t|D ]\}}t|dkr]|ddt|d   d||< qBt|D ]\}}|t|||   t|D ]}|d t|kr|t|kr|dt|d d	 dt|d     ||| kr|||   |||  d 7  < qv||  || d|d	 t||  d   7  < qv|t|kr|dt|d d	 dt|d     ||  d|d	 d  7  < qvqctddd |D S )Nr   )Vectorz:ASCII pretty printing of BasisDependent is not implementedc                 S   s   | d   S Nr   )__str__r  r>   r>   r?   r  f      z5PrettyPrinter._print_BasisDependent.<locals>.<lambda>r   r_   r   r]  z(-1) r   r  r  
u   ⎟u   ⎠c                 S   s   g | ]}| d qS )r  )splitra  r   r>   r>   r?   rd        z7PrettyPrinter._print_BasisDependent.<locals>.<listcomp>c                 S   s   g | ]}t |qS r>   )r  r  r>   r>   r?   rd    s    c                 S   s   g | ]}|d d qS )Nr>   )ra  r   r>   r>   r?   rd        )sympy.vectorr  rH   NotImplementedErrorzeror   _pretty_formr6   separateitemsr   
componentsr   r%  rI   rT   
startswithr  r   r  r  rfindr   insertrD  join)r<   rD   r  o1vectstrsr  systemvect
inneritemsr   varg_strlengthsstrsflagr)   partstrtempstrparenindex
n_newlinespartsr4   r>   r>   r?   _print_BasisDependentV  s   








$
 z#PrettyPrinter._print_BasisDependentc           	         sd  ddl m  | dkr| |d S g gdd t| D  }dd |jD } fdd}tj| D ]e}|d	 ||  d
}t| d d	d	D ]M}t	||d  |j| k r\ n=|rj|| ||d   n%|| |||d   t	||d  dkr||| d	 gg|| d	< | }g ||d < qKq4|d d }| d dkr||g}| |S )Nr   ImmutableMatrixr>   c                 S   s   g | ]}g qS r>   r>   r`  r>   r>   r?   rd    r  z2PrettyPrinter._print_NDimArray.<locals>.<listcomp>c                 S   s   g | ]}t t|qS r>   )r   r  r`  r>   r>   r?   rd    r  c                    s    | ddS )NFr  r>   r  r-  r>   r?   r    r
  z0PrettyPrinter._print_NDimArray.<locals>.<lambda>r]  Tr_   r   )
sympy.matrices.immutabler.  rankrI   r  r  	itertoolsproductr%  r  )	r<   rD   	level_strshape_rangesr{  outer_ievenback_outer_iout_exprr>   r-  r?   _print_NDimArray  s8   



zPrettyPrinter._print_NDimArrayc              	   C   sn  t |}t d|  }t d|  }d }d }t|D ]\}	}
| |
jd }|
|v s.|rG||
jkrG|
jr?tt |d }ntt |d }|
|v rctt |d }tt || ||
  }d}nd}|
jrt || }t |d|   }t |d|   }nt || }t |d|   }t |d|   }|
j}qt|	| }t|
| }|S )Nr   r   r   =TF)r   r   r  rI   rS   is_upr   r   ri   r   r   )r<   rY   indices	index_mapcentertopbotlast_valenceprev_mapr)   r)  indpicpictr>   r>   r?   _printer_tensor_indices  s6   z%PrettyPrinter._printer_tensor_indicesc                 C   s    |j d j}| }| ||S r  )rS   rY   get_indicesrE  )r<   rD   rY   r<  r>   r>   r?   _print_Tensor   s   zPrettyPrinter._print_Tensorc                 C   s,   |j jd j}|j  }|j}| |||S r  )rD   rS   rY   rF  r=  rE  )r<   rD   rY   r<  r=  r>   r>   r?   _print_TensorElement  s   
z"PrettyPrinter._print_TensorElementc                    s>   |  \}} fdd|D }tj| }|rt|| S |S )Nc                    8   g | ]}t |td  k rt |  n |qS r   r   r   r   rI   rT   r`  rG   r>   r?   rd        z0PrettyPrinter._print_TensMul.<locals>.<listcomp>)!_get_args_for_traditional_printerr   r  rU   )r<   rD   r  rS   rW   r>   rG   r?   _print_TensMul  s   

zPrettyPrinter._print_TensMulc                    s    fdd|j D }tj| S )Nc                    rI  r   rJ  r`  rG   r>   r?   rd    rK  z0PrettyPrinter._print_TensAdd.<locals>.<listcomp>)rS   r   __add__)r<   rD   rS   r>   rG   r?   _print_TensAdd  s   

zPrettyPrinter._print_TensAddc                 C   s    |j d }|js| }| |S r  )rS   r;  rI   )r<   rD   r   r>   r>   r?   _print_TensorIndex   s   

z PrettyPrinter._print_TensorIndexc           	      C   s   | j rtd}nd}d }t|jD ]#}| |}t|| }|d u r&|}qt|d }t|| }qt| |j	 dtj
i}t|}t|jdkrX|| t|j }t|tj| }|jd |_tt|| }tj|_|S )Nr   r   r   r   r_   )rH   r"   r   	variablesrI   r   rU   ri   rD   rT   r   r  r   r   r   r   r   r   r   )	r<   r   r   r   variabler   r   r   rW   r>   r>   r?   _print_PartialDerivative&  s0   

z&PrettyPrinter._print_PartialDerivativec                    s  i  t |jD ]-\}}| |j |df< |jdkr#td |df< qttd| |j  |df< qd}d}t|j fddtdD }d }tD ]p}d }	tdD ]K}
 ||
f }|	 ||
 ksjJ ||
 |	  }|d }|| }t|d	|  }t|
d	|  }|	d u r|}	qXt|	d	|  }	t|	| }	qX|d u r|	}qPt|D ]	}t|d	 }qt||	 }qPt|d
d }| d |_tj|_|S )Nr   T	otherwiser_   zfor r   c                    s(   g | ] t  fd dtD qS )c                    r^  r>   r_  r`  )Pr4   r>   r?   rd  U  re  z=PrettyPrinter._print_Piecewise.<locals>.<listcomp>.<listcomp>)r   r  ra  rU  len_args)r4   r?   rd  U  s     z2PrettyPrinter._print_Piecewise.<locals>.<listcomp>r   {r   )r  rS   rI   rD   condr   ri   r  r  r   rU   r   rT   r  r   r   r   )r<   pexprr   ecri  rj  rk  rl  r)   rm  r4   prn  ro  rp  r   r>   rW  r?   _print_PiecewiseF  sP   

zPrettyPrinter._print_Piecewisec                 C   s   ddl m} | ||S )Nr   )	Piecewise)$sympy.functions.elementary.piecewiser_  rI   rewrite)r<   iter_  r>   r>   r?   
_print_ITE~  s   zPrettyPrinter._print_ITEc                 C   sP   d }|D ]}|}|d u r|}qt |d }t || }q|d u r&td}|S )Nr  r   )r   ri   r   )r<   r!  rl  r  r]  r>   r>   r?   _hprint_vec  s   zPrettyPrinter._hprint_vecr   c           	      C   sj   |r| j s| j|d|f|||ddS | j||f|||d}ttd| |jd}| j|||f|||dS )Nr   T)rU   ri   r  ifascii_nougly)rU   ri   r  r   )rH   rR   r   r   r  r   )	r<   p1p2rU   ri   r  re  tmpsepr>   r>   r?   _hprint_vseparator  s   
z PrettyPrinter._hprint_vseparatorc                    s   fdd|j D } fdd|jD } |j}| d |_d }||fD ]} |}|d u r5|}q't|d }t|| }q'| d |_t|	d }t|
d } ||}t|dd }| d d }| | d }	td	\}
}}}}td
||  | d
|	|   ||
 d}|
d d }t|	 t|j  }t|
 t|j }|| |_t|
d| }|S )Nc                       g | ]}  |qS r>   r6  ra  r  rG   r>   r?   rd    r  z.PrettyPrinter._print_hyper.<locals>.<listcomp>c                    rl  r>   r6  ra  brG   r>   r?   rd    r  r   r   rc   rd   r_   Fr  rf  )apbqrI   argumentr  r   rd  r   r   rU   ri   rk  rT   r$   r  )r<   rN   rq  rr  rU  rl  r!  rm  r   r   sztro  addimgrp  r>   rG   r?   _print_hyper  s8   

zPrettyPrinter._print_hyperc                     s  i } fdd|j D |d<  fdd|jD |d<  fdd|jD |d<  fdd|jD |d	<  |j}| d
 |_i }|D ]} || ||< qCt	d
D ]H}t
|d|f  |d|f  }t	d
D ]0}|||f }	||	  d
 }
||
 |	  }t|	d|
  }	t|	d|  }	|	|||f< qjqSt|d d|d  }t|d }t|d d|d	  }t|| }| d
 |_t|d }t|d } ||}t|dd }| d
 d }| | d }td\}}}}}td||  | d||   || d} t|j} t|j} t|j} t|j }dd }|||\}}|||\}}t|d| }t|d| }|j| d
 }|dkrit|d|  }t|| }||_t|| }|| |_t|d| }|S )Nc                    rl  r>   r6  rm  rG   r>   r?   rd    r  z0PrettyPrinter._print_meijerg.<locals>.<listcomp>r  c                    rl  r>   r6  rm  rG   r>   r?   rd    r  )r   r_   c                    rl  r>   r6  rn  rG   r>   r?   rd    r  )r_   r   c                    rl  r>   r6  rn  rG   r>   r?   rd    r  r  r   r   r_   r   z  rc   rd   Gr  rf  c                 S   sV   |   |   }|dkr| |fS |dkr| t|d|  fS t| d|   |fS )Nr   r   )r   r   rU   )rg  rh  diffr>   r>   r?   rB    s   z,PrettyPrinter._print_meijerg.<locals>.adjustr  )anaotherbmbotherrI   rs  r  r   rd  r  r   r   r   rU   ri   r   rk  rT   r$   r  rq  rr  ) r<   rN   r!  rU  vpidxr)   rk  r4   r   rU   ri   D1D2rl  r   r   rt  ru  ro  rv  rw  rp  pppqpmpnrB  puplhtr]  r>   rG   r?   _print_meijerg  sj   "

zPrettyPrinter._print_meijergc                 C   s"   t tdd}|| |jd  S )NExp1rN   r   )r   r   rI   rS   )r<   rN   r  r>   r>   r?   _print_ExpBase  s   zPrettyPrinter._print_ExpBasec                 C   s   t tddS )Nr  rN   )r   r   rM   r>   r>   r?   _print_Exp1$     zPrettyPrinter._print_Exp1rc   rd   c                 C   s   | j |j|j||||dS )N)r   	func_namerU   ri   )_helper_print_functionr|   rS   )r<   rN   r   r  rU   ri   r>   r>   r?   r   '  s   zPrettyPrinter._print_Functionc                 C      | j |ddS NCr  r   rM   r>   r>   r?   _print_mathieuc-  r  zPrettyPrinter._print_mathieucc                 C   r  Nr   r  r  rM   r>   r>   r?   _print_mathieus0  r  zPrettyPrinter._print_mathieusc                 C   r  )NzC'r  r  rM   r>   r>   r?   _print_mathieucprime3  r  z"PrettyPrinter._print_mathieucprimec                 C   r  )NzS'r  r  rM   r>   r>   r?   _print_mathieusprime6  r  z"PrettyPrinter._print_mathieusprimer  c	                 C   s   |rt |td}|st|dr|j}|r| t|}	n	t| |  }	|rB| jr/t	d}
nd}
| |
}
tt
|	|
dtji}	t| j||dj||d }tt
|	|dtji}|	|_||_|S )Nr   r   zModifier Letter Low Ringr  r   r  r  )r   r   hasattrr   rI   r   r   rT   rH   r   r   r   r   rR   r   r  r  )r<   r|   rS   r   r  r  elementwiserU   ri   r  r  r  rW   r>   r>   r?   r  9  s8   



z$PrettyPrinter._helper_print_functionc                 C   s$   |j }|j}|g}| j||dddS )Nr   T)r  r  )r  rD   r  )r<   rN   r|   r   rS   r>   r>   r?   _print_ElementwiseApplyFunction^  s   z-PrettyPrinter._print_ElementwiseApplyFunctionc                 C   s   ddl m} ddlm}m} ddlm} ddlm} ddl	m
} ddlm} |td dg|td	 d	g|td
 dg|td dg|td dg|td dg|ddgiS )Nr   )KroneckerDelta)gamma
lowergamma)lerchphi)beta)
DiracDelta)ChideltaGammaPhir  r  Betar  r  )(sympy.functions.special.tensor_functionsr  'sympy.functions.special.gamma_functionsr  r  &sympy.functions.special.zeta_functionsr  &sympy.functions.special.beta_functionsr  'sympy.functions.special.delta_functionsr  'sympy.functions.special.error_functionsr  r!   )r<   r  r  r  r  r  r  r  r>   r>   r?   _special_function_classesd  s   z'PrettyPrinter._special_function_classesc                 C   sf   | j D ]&}t||r)|j|jkr)| jrt| j | d   S t| j | d   S q|j}tt|S )Nr   r_   )r  
issubclassr   rH   r   r   )r<   rD   clsr  r>   r>   r?   _print_FunctionClasst  s   
z"PrettyPrinter._print_FunctionClassc                 C   
   |  |S rA   )rE   rC   r>   r>   r?   _print_GeometryEntity~  s   
z#PrettyPrinter._print_GeometryEntityc                 C       | j rtd nd}| j||dS )Nr  r  r  rH   r!   r   r<   rN   r  r>   r>   r?   _print_lerchphi     zPrettyPrinter._print_lerchphic                 C   r  )Netadirichlet_etar  r  r  r>   r>   r?   _print_dirichlet_eta  r  z"PrettyPrinter._print_dirichlet_etac                 C   sX   | j rtd nd}|jd dkr%t| |jd   }t|| }|S | j||dS )Ntheta	Heavisider_   g      ?r   r  )rH   r!   rS   r   rI   rT   rU   r   )r<   rN   r  rW   r>   r>   r?   _print_Heaviside  s   zPrettyPrinter._print_Heavisidec                 C   r  r  r  rM   r>   r>   r?   _print_fresnels  r  zPrettyPrinter._print_fresnelsc                 C   r  r  r  rM   r>   r>   r?   _print_fresnelc  r  zPrettyPrinter._print_fresnelcc                 C   r  )NAir  r  rM   r>   r>   r?   _print_airyai  r  zPrettyPrinter._print_airyaic                 C   r  )NBir  r  rM   r>   r>   r?   _print_airybi  r  zPrettyPrinter._print_airybic                 C   r  )NzAi'r  r  rM   r>   r>   r?   _print_airyaiprime  r  z PrettyPrinter._print_airyaiprimec                 C   r  )NzBi'r  r  rM   r>   r>   r?   _print_airybiprime  r  z PrettyPrinter._print_airybiprimec                 C   r  )NWr  r  rM   r>   r>   r?   _print_LambertW  r  zPrettyPrinter._print_LambertWc                 C   r  )NCovr  r  rM   r>   r>   r?   _print_Covariance  r  zPrettyPrinter._print_Covariancec                 C   r  )NVarr  r  rM   r>   r>   r?   _print_Variance  r  zPrettyPrinter._print_Variancec                 C   r  )NrU  r  r  rM   r>   r>   r?   _print_Probability  r  z PrettyPrinter._print_Probabilityc                 C   s   | j |ddddS )NrY  rr  rs  )r  rU   ri   r  rM   r>   r>   r?   _print_Expectation  s   z PrettyPrinter._print_Expectationc                 C   sb   |j }|j}| jrd}nd}t|dkr|d jr|d }| |}tt||| |ddiS )Nu    ↦  -> r_   r   r   rE  )	rD   	signaturerH   r  	is_symbolrI   r   r   r   )r<   rN   rD   sigarrowvar_formr>   r>   r?   _print_Lambda  s   
zPrettyPrinter._print_Lambdac                 C   s  |  |j}|jrtdd |jD st|jdkrxt|d }t|jdkr4t||  |j }nt|jrFt||  |jd  }| jrQt|d }nt|d }t|jdkrkt||  |j }nt||  |jd  }t|	  }t|
d }|S )	Nc                 s   s    | ]}|t jkV  qd S rA   )r   Zero)ra  r]  r>   r>   r?   	<genexpr>      z-PrettyPrinter._print_Order.<locals>.<genexpr>r_   ; r   u    → r  O)rI   rD   pointanyr  rQ  r   ri   rH   rT   rU   r<   rD   rW   r>   r>   r?   _print_Order  s$   
zPrettyPrinter._print_Orderc                 C   s   | j r0| |jd |jd  }| |jd }td}t|| }t|d }|| }|S | |jd }| |jd |jd  }| |ddd}|| S )Nr   r_   r   r;  r<  r   )rH   rI   rS   r   ri   rR   )r<   rN   shiftr   r  rW   r>   r>   r?   _print_SingularityFunction  s   z(PrettyPrinter._print_SingularityFunctionc                 C   r  )Nr  r  r  r  r  r>   r>   r?   _print_beta  r  zPrettyPrinter._print_betac                 C      d}| j ||dS )NzB'r  r  r  r>   r>   r?   _print_betainc     zPrettyPrinter._print_betaincc                 C   r  )Nr  r  r  r  r>   r>   r?   _print_betainc_regularized  r  z(PrettyPrinter._print_betainc_regularizedc                 C       | j rtd nd}| j||dS Nr  r  r  r  r>   r>   r?   _print_gamma  r  zPrettyPrinter._print_gammac                 C   r  r  r  r  r>   r>   r?   _print_uppergamma  r  zPrettyPrinter._print_uppergammac                 C   r  )Nr  r  r  r  r  r>   r>   r?   _print_lowergamma  r  zPrettyPrinter._print_lowergammac                 C   s   | j rYt|jdkr@ttd }| |jd }t|  }| |jd }t|  }|| }t|d }t|| }|S | |jd }t|  }t|td  }|S | 	|S )Nr   r  r_   r   r   )
rH   r  rS   r   r!   rI   rT   ri   rU   r   )r<   rN   r  ro  crW   r>   r>   r?   _print_DiracDelta  s    
zPrettyPrinter._print_DiracDeltac                 C   s>   |j d jr| jr| td|j d  |j d S | |S )Nr   zE_%sr_   )rS   r   rH   r   r   rM   r>   r>   r?   _print_expint  s   "
zPrettyPrinter._print_expintc                 C   sD   t d}t | |j  }t t||dt ji}||_||_|S )Nr  r   )	r   rR   rS   rT   r   r   r   r  r  )r<   rN   r  r  rW   r>   r>   r?   
_print_Chi  s   
zPrettyPrinter._print_Chic                 C   s^   |  |jd }t|jdkr|}n|  |jd }| ||}t|  }t|d }|S )Nr   r_   rY  )rI   rS   r  rk  r   rT   rU   )r<   rN   pforma0rW   pforma1r>   r>   r?   _print_elliptic_e$  s   zPrettyPrinter._print_elliptic_ec                 C   s.   |  |jd }t|  }t|d }|S )Nr   K)rI   rS   r   rT   rU   rV   r>   r>   r?   _print_elliptic_k/  s   zPrettyPrinter._print_elliptic_kc                 C   sJ   |  |jd }|  |jd }| ||}t|  }t|d }|S )Nr   r_   rp  )rI   rS   rk  r   rT   rU   )r<   rN   r  r  rW   r>   r>   r?   _print_elliptic_f5  s   zPrettyPrinter._print_elliptic_fc                 C   s   | j rtd nd}| |jd }| |jd }t|jdkr'| ||}n| |jd }| j||dd}t|d }t|| }t|  }t|| }|S )NPir   r_   r   Fre  r  )	rH   r!   rI   rS   r  rk  r   rU   rT   )r<   rN   rY   r  r  rW   pforma2pformar>   r>   r?   _print_elliptic_pi=  s   z PrettyPrinter._print_elliptic_pic                 C       | j r	ttdS | tdS )NphiGoldenRatiorH   r   r   rI   r   rC   r>   r>   r?   _print_GoldenRatioL     z PrettyPrinter._print_GoldenRatioc                 C   r  )Nr  
EulerGammar  rC   r>   r>   r?   _print_EulerGammaQ  r   zPrettyPrinter._print_EulerGammac                 C   s   |  tdS )Nry  )rI   r   rC   r>   r>   r?   _print_CatalanV  r  zPrettyPrinter._print_Catalanc                 C   s\   |  |jd }|jtjkrt|  }t|d }t||  |jd  }tj|_|S )Nr   z mod r_   )rI   rS   r   r   r   rT   ri   r   r  r>   r>   r?   
_print_ModY  s   zPrettyPrinter._print_Modc                 C   s  | j ||d}g g }}dd }t|D ]z\}}|jrM| rM|jdd\}	}
|	dkr3t|
ddi}nt|	 g|
R ddi}| |}|||| q|jr`|j	dkr`|d  || q|j
rv|d	k rv| | }|||| q|jr|t| |   q|| | q|rd
}|D ]}|d ur| dkr nqd}|D ]4}|| d}}|d	k r| d
}}|rtt|jtt|j	 }n| |}|r|||}|||< qtj| S )Nr*   c                 S   sj   |dkr|   dkrd}nd}nd}| jtjks| jtjkr%t|   }n| }t||}t|dtjiS )z'Prepend a minus sign to a pretty form. r   r_   z- r!  r  r   )r  r   r   NEGADDr   rT   r   )rW   r)  	pform_negr]  r>   r>   r?   pretty_negativef  s   
z1PrettyPrinter._print_Add.<locals>.pretty_negativeF)rationalr]  r  r_   r   T)_as_ordered_termsr  is_Mulr  as_coeff_mulr   rI   r%  is_Rationalq	is_Numberis_Relationalr   rT   r  r8   r]  rN  )r<   rD   r*   termspformsr<  r	  r)   r#  r  othernegtermrW   largenegativer>   r>   r?   
_print_Addb  sL   






zPrettyPrinter._print_Addc           	         s  ddl m  |j}|d tju stdd |dd  D rIttj|}|d dk}|r5t	ddd|d< t	j
| }|rGt	d|j |j|j}|S g }g }jd	vrW| }nt|j}t| fd
dd}|D ]W}|jr|jr|jjr|jjr|jdkr|t|j|j dd qh|t|j|j  qh|jr|tjur|jdkr|t|j |jdkr|t|j qh|| qhfdd|D }fdd|D }t|dkrt	j
| S t|dkr|tj t	j
| t	j
|  S )Nr   Quantityc                 s   s    | ]}t |tV  qd S rA   )r6   r   ra  r   r>   r>   r?   r    r  z+PrettyPrinter._print_Mul.<locals>.<genexpr>r_   z-1r  r!  )oldnonec                    s    t |  pt | tot | j S rA   )r6   r
   r  r  r  r>   r?   r    s   
 z*PrettyPrinter._print_Mul.<locals>.<lambda>r   r]  Fr  c                    rl  r>   r6  )ra  airG   r>   r?   rd    r  z,PrettyPrinter._print_Mul.<locals>.<listcomp>c                    rl  r>   r6  )ra  birG   r>   r?   rd    r  )sympy.physics.unitsr  rS   r   Oner  r   maprI   r   r  r   r   r   r*   as_ordered_factorsr   is_commutativeis_Powr  r  is_negativer%  r
   r  rT  r]  r	   r  r  )	r<   r2  rS   strargsnegoneobjr  ro  r  r>   )r  r<   r?   r    sH   (







zPrettyPrinter._print_Mulc           	         st  |  |}| jd r*| jr*|dkr*| dkr*| dks#|jr*|jr*t|d S t	dd t	dd  }|  |}| dkrM|  ||  d|  S |dkrSdnt
|d}t|dkrjdt|d  | }t|d	 | }d
|_| d td	 fddtD }d |_t|| }td|j|_ttdd|  }t|| }t|| }|S )Nr/   r   r_   u   √rC  \r   r   r  r   c                 3   s,    | ]}d | d    d |  V  qdS )r   r_   Nr>   r`  _zZ
linelengthr>   r?   r    s
    
z0PrettyPrinter._print_nth_root.<locals>.<genexpr>r   )rI   r7   rH   r  r   r   r   r   rU   r   r8   ljustr  r   r   r  r  ri   r   r   r   )	r<   r  rootbprettyrootsignrprettyr  diagonalr   r>   r+  r?   _print_nth_root  sD   






zPrettyPrinter._print_nth_rootc                 C   s   ddl m} | \}}|jrU|tju rtd| | S ||\}}|tju r?|j	r?|j
s?|js4|jr?| jd r?| ||S |jrU|dk rUtd| t|| dd S |jrgt| |  | |S | || | S )Nr   )fractionr  r0   Fr  )sympy.simplify.simplifyr5  as_base_expr$  r   NegativeOner   rI   r!  is_Atomr   r  r   r7   r4  r
   r  rT   __pow__)r<   powerr5  ro  rN   r   r   r>   r>   r?   
_print_Pow  s   
"zPrettyPrinter._print_Powc                 C   s   |  |jd S r  )rI   rS   rC   r>   r>   r?   _print_UnevaluatedExpr%     z$PrettyPrinter._print_UnevaluatedExprc                 C   s   |dkr|dk rt t|t jdS t t|S t|dkrBt|dkrB|dk r6t t|t jdt t| S t t|t t| S d S )Nr_   r   )r   
   )r   r8   r  abs)r<   r]  r  r>   r>   r?   __print_numer_denom(  s   z!PrettyPrinter.__print_numer_denomc                 C   &   |  |j|j}|d ur|S | |S rA   )!_PrettyPrinter__print_numer_denomr]  r  rE   r<   rD   r  r>   r>   r?   _print_Rational:     
zPrettyPrinter._print_Rationalc                 C   rB  rA   )rC  	numeratordenominatorrE   rD  r>   r>   r?   _print_FractionB  rF  zPrettyPrinter._print_Fractionc                 C   sd   t |jdkrt|js| |jd | t |j S | jr!dnd}| j|jd d d| dd dS )	Nr_   r      ×r   r   c                 S      | j p| jp| jS rA   )is_Unionis_Intersectionis_ProductSetsetr>   r>   r?   r  P      z1PrettyPrinter._print_ProductSet.<locals>.<lambda>r  )r  setsr   rI   rH   rR   )r<   r]  	prod_charr>   r>   r?   _print_ProductSetJ  s    zPrettyPrinter._print_ProductSetc                 C   s   t |jtd}| |dddS )Nr   rY  }r  )r   rS   r   rR   )r<   r   r  r>   r>   r?   _print_FiniteSetS  s   zPrettyPrinter._print_FiniteSetc                 C   s   | j rd}nd}|jjr$|jjr$|jjr|ddd|f}nF|ddd|f}n>|jjr5||d |j |d f}n-|jjrGt|}t|t||f}nt|dkr^t|}t|t|||d f}nt	|}| 
|ddd	S )
N   …...r]  r   r_   r  rY  rU  r  )rH   startis_infinitestopstepis_positiveiterr   r  r   rR   )r<   r   dotsprintsetitr>   r>   r?   _print_RangeW  s"   zPrettyPrinter._print_Rangec                 C   s\   |j |jkr| |jd d ddS |jrd}nd}|jr d}nd}| |jd d ||S )	Nr_   rY  rU  rc   rr  rd   rs  r   )rY  endrR   rS   	left_open
right_openr<   r)   rU   ri   r>   r>   r?   _print_Intervalp  s   zPrettyPrinter._print_Intervalc                 C   s    d}d}|  |jd d ||S )Nr;  r<  r   rR   rS   rf  r>   r>   r?   _print_AccumulationBounds  s   z'PrettyPrinter._print_AccumulationBoundsc                 C   (   dt dd }| j|jd d |dd dS )Nr   Intersectionr   c                 S   rK  rA   )rN  rL  is_ComplementrO  r>   r>   r?   r    rQ  z3PrettyPrinter._print_Intersection.<locals>.<lambda>r  r   rR   rS   r<   r  r  r>   r>   r?   _print_Intersection     z!PrettyPrinter._print_Intersectionc                 C   rj  )Nr   Unionr"   c                 S   rK  rA   )rN  rM  rl  rO  r>   r>   r?   r    rQ  z,PrettyPrinter._print_Union.<locals>.<lambda>r  rm  )r<   r  union_delimiterr>   r>   r?   _print_Union  rp  zPrettyPrinter._print_Unionc                 C   s,   | j stddtd }| |jd d |S )Nz?ASCII pretty printing of SymmetricDifference is not implementedr   SymmetricDifference)rH   r  r   rR   rS   )r<   r  sym_delimeterr>   r>   r?   _print_SymmetricDifference  s   z(PrettyPrinter._print_SymmetricDifferencec                 C   s   d}| j |jd d |dd dS )Nz \ c                 S   rK  rA   )rN  rM  rL  rO  r>   r>   r?   r    s    z1PrettyPrinter._print_Complement.<locals>.<lambda>r  rh  rn  r>   r>   r?   _print_Complement  s   zPrettyPrinter._print_Complementc                    s   | j rd nd |j}|j}|j}| |j}t|dkr6| j|d  |d fdd}| j||ddd	dd
S t	 fddt
||D }| j|d d dd}| j||ddd	dd
S )N   ∊inr_   r   r   r  rY  rU  TrU   ri   re  r  c                 3   s.    | ]\}}|d  d |dfD ]}|V  qqdS )r   r  Nr>   )ra  r  setvr4   innr>   r?   r    s   
 z0PrettyPrinter._print_ImageSet.<locals>.<genexpr>r]  r   )rH   r  	base_setsr  rI   rD   r  rR   rk  r   r  )r<   tsfunrR  r  rD   r   pargsr>   r|  r?   _print_ImageSet  s*   zPrettyPrinter._print_ImageSetc           	      C   s   | j rd}d}nd}d}| t|j}t|jdd }|d ur(| |j }n| |j}| j r<| |}t|	  }|j
tju rM| j||dddd	d
S | |j
}| j|||||fd	d}| j||dddd	d
S )Nrx  r   ry  andas_exprrY  rU  Tr   rz  r  )rH   rR   r   r   getattr	conditionrI   r  r   rT   base_setr   UniversalSetrk  )	r<   r  r}  _andrQ  r  rZ  r  r  r>   r>   r?   _print_ConditionSet  s2   

z!PrettyPrinter._print_ConditionSetc                 C   s^   | j rd}nd}| |j}| |j}| |j}| j|||fdd}| j||dddddS )	Nrx  ry  r   r  rY  rU  Trz  )rH   rR   rQ  rI   rD   rR  rk  )r<   r  r}  rQ  rD   prodsetsr  r>   r>   r?   _print_ComplexRegion  s   z"PrettyPrinter._print_ComplexRegionc                 C   sD   |j \}}| jrd}tt| ||| |ddiS tt|S )Nu    ∈ r   rE  )rS   rH   r   r   r   rI   r   )r<   rN   r  rP  elr>   r>   r?   _print_Contains  s   

zPrettyPrinter._print_Containsc                 C   sP   |j jtju r|jjtju r| |jS | jrd}nd}| |	 | | S )NrW  rX  )
r{  formular   r  bnrI   a0rH   r  truncate)r<   r   r_  r>   r>   r?   _print_FourierSeries  s   z"PrettyPrinter._print_FourierSeriesc                 C      |  |jS rA   )r  infiniter<   r   r>   r>   r?   _print_FormalPowerSeries	  rF   z&PrettyPrinter._print_FormalPowerSeriesc                 C   s0   t | |j  }| td}t || S )NSetExpr)r   rI   rP  rT   r   ri   )r<   se
pretty_setpretty_namer>   r>   r?   _print_SetExpr	  s   zPrettyPrinter._print_SetExprc                 C   s   | j rd}nd}t|jjdkst|jjdkrtd|jtju r?|j}|||d ||d ||d ||f}n|jtj	u sJ|j
dkrZ|d d }|| t|}nt|}| |S )	NrW  rX  r   z@Pretty printing of sequences with symbolic bound not implementedr  r   r_   r  )rH   r  rY  free_symbolsr[  r  r   rU  r  rT  lengthr%  r   _print_list)r<   r   r_  r[  r`  r>   r>   r?   _print_SeqFormula	  s     


zPrettyPrinter._print_SeqFormulac                 C   s   dS )NFr>   r  r>   r>   r?   r  %	  s    zPrettyPrinter.<lambda>c              	   C   s   z2g }|D ]}|  |}	||rt|	  }	|r|| ||	 q|s*td}
nttj|  }
W n> typ   d }
|D ](}| |}	||rNt|	  }	|
d u rU|	}
q=tt|
| }
tt|
|	 }
q=|
d u rntd}
Y nw t|
j|||d }
|
S )Nr   r  )rI   r   rT   r%  r   r   AttributeErrorrK   )r<   seqrU   ri   r  r  re  r  r  rW   r   r>   r>   r?   rR   $	  s:   



zPrettyPrinter._print_seqc                 C   sL   d }|D ]}|d u r|}qt || }t || }q|d u r$t dS |S )Nr   )r   ri   )r<   r  rS   rW   r   r>   r>   r?   r  M	  s   zPrettyPrinter.joinc                 C      |  |ddS r  rR   )r<   r   r>   r>   r?   r  \	  r  zPrettyPrinter._print_listc                 C   sH   t |dkrtt| |d d }t|jdddd S | |ddS )Nr_   r   r   rc   rd   Tr  )r  r   r   r   rI   rT   rR   )r<   ru  ptupler>   r>   r?   _print_tuple_	  s   zPrettyPrinter._print_tuplec                 C   r  rA   )r  rC   r>   r>   r?   _print_Tuplef	     
zPrettyPrinter._print_Tuplec                 C   s`   t | td}g }|D ]}| |}| || }tt|d| }|| q| |ddS )Nr   z: rY  rU  )	r   keysr   rI   r   r   r   r%  rR   )r<   r   r  r  r   r  Vr   r>   r>   r?   _print_dicti	  s   
zPrettyPrinter._print_dictc                 C   r  rA   )r  )r<   r   r>   r>   r?   _print_Dictv	  r  zPrettyPrinter._print_Dictc                 C   s:   |st dS t|td}| |}t |jdddd }|S )Nzset()r   rY  rU  Tr  )r   r   r   rR   rT   r<   r   r  prettyr>   r>   r?   
_print_sety	  s   
zPrettyPrinter._print_setc                 C   sd   |st dS t|td}| |}t |jdddd }t |jdddd }t tt|j| }|S )	Nzfrozenset()r   rY  rU  Tr  rc   rd   )	r   r   r   rR   rT   r   r   typer   r  r>   r>   r?   _print_frozenset	  s   
zPrettyPrinter._print_frozensetc                 C   r  )Nu   𝕌r  r  r  r>   r>   r?   _print_UniversalSet	  r  z!PrettyPrinter._print_UniversalSetc                 C   r@   rA   r   r   )r<   ringr>   r>   r?   _print_PolyRing	  rF   zPrettyPrinter._print_PolyRingc                 C   r@   rA   r  )r<   fieldr>   r>   r?   _print_FracField	  rF   zPrettyPrinter._print_FracFieldc                 C   r@   rA   rB   )r<   elmr>   r>   r?   _print_FreeGroupElement	  rF   z%PrettyPrinter._print_FreeGroupElementc                 C   r@   rA   r  )r<   polyr>   r>   r?   _print_PolyElement	  rF   z PrettyPrinter._print_PolyElementc                 C   r@   rA   r  )r<   fracr>   r>   r?   _print_FracElement	  rF   z PrettyPrinter._print_FracElementc                 C   s&   |j r| |  S | | S rA   )
is_aliasedrI   as_polyr  rC   r>   r>   r?   _print_AlgebraicNumber	  s   z$PrettyPrinter._print_AlgebraicNumberc                 C   s:   | j |jdd|jg}t| |  }t|d }|S )Nlexr  CRootOf)r  rD   r)  r   rR   rT   rU   r<   rD   rS   rW   r>   r>   r?   _print_ComplexRootOf	  s   z"PrettyPrinter._print_ComplexRootOfc                 C   sT   | j |jddg}|jtjur|| |j t| |	  }t|
d }|S )Nr  r  RootSum)r  rD   r  r   IdentityFunctionr%  rI   r   rR   rT   rU   r  r>   r>   r?   _print_RootSum	  s   zPrettyPrinter._print_RootSumc                 C   s"   | j rd}nd}tt||j S )Nu   ℤ_%dzGF(%d))rH   r   r   mod)r<   rD   formr>   r>   r?   _print_FiniteField	  s   z PrettyPrinter._print_FiniteFieldc                 C   r  )Nu   ℤZZr  rC   r>   r>   r?   _print_IntegerRing	  r  z PrettyPrinter._print_IntegerRingc                 C   r  )Nu   ℚQQr  rC   r>   r>   r?   _print_RationalField	  r  z"PrettyPrinter._print_RationalFieldc                 C   :   | j rd}nd}|jrt|S | t|d t|j S )Nu   ℝRRr   rH   has_default_precisionr   rI   r   r8   	precisionr<   domainprefixr>   r>   r?   _print_RealField	     zPrettyPrinter._print_RealFieldc                 C   r  )Nu   ℂCCr   r  r  r>   r>   r?   _print_ComplexField	  r  z!PrettyPrinter._print_ComplexFieldc                 C   ^   t |j}|jjsttd| |j }|| | |dd}t|	| |j
 }|S Norder=rr  rs  r   symbolsr*   
is_defaultr   ri   rI   r%  rR   rU   r  r<   rD   rS   r*   rW   r>   r>   r?   _print_PolynomialRing	     

z#PrettyPrinter._print_PolynomialRingc                 C   r  )Nr  rc   rd   r  r  r>   r>   r?   _print_FractionField	  r  z"PrettyPrinter._print_FractionFieldc                 C   sV   |j }t|jt|jkr|dt|j f }| |dd}t|| |j }|S r  )	r  r8   r*   default_orderrR   r   rU   rI   r  )r<   rD   grW   r>   r>   r?   _print_PolynomialRingBase	  s   z'PrettyPrinter._print_PolynomialRingBasec                    s    fdd j D }td|jddd }fdd jD }ttd j }ttd	 j }d|g| ||g }t|  }t|	 j
j }|S )
Nc                    s   g | ]
}j | jd qS )r  )r  r*   r  basisr<   r>   r?   rd  
  s    z6PrettyPrinter._print_GroebnerBasis.<locals>.<listcomp>r  rr  rs  r  c                    rl  r>   r6  )ra  genrG   r>   r?   rd  
  r  zdomain=r  )exprsr   r  rT   gensri   rI   r  r*   rU   r   r   )r<   r  r  r  r  r*   rW   r>   r  r?   _print_GroebnerBasis
  s   z"PrettyPrinter._print_GroebnerBasisc              	      s     |j}t|  }| dkr| nd}ttd||jd}t|| }|j}| d |_t| 	 fddt
|j|jD  }||_|S )Nr_   r   r   rf  c              	      s8   g | ]} j  |d  td |d fddqS )r   r4  r_   r   r  )rR   rI   r   )ra  r!  rG   r>   r?   rd  
  s    $z-PrettyPrinter._print_Subs.<locals>.<listcomp>)rI   rD   r   rT   r  r   r   r   ri   rR   r  rQ  r  )r<   rN   rW   r  rvertro  r>   rG   r?   _print_Subs
  s   zPrettyPrinter._print_Subsc           
      C   s   t |}| |jd }t d|  }t || }t || }t|jdkr+|S |j\}}|}t | |g  }	t t	
||	dt ji}||_|	|_|S )Nr   r   r_   r   )r   rI   rS   r   r   ri   r  rR   rT   r   r   r   r  r  )
r<   rN   rY   rW   r   r   r  r   r  r  r>   r>   r?   _print_number_function&
  s$   

z$PrettyPrinter._print_number_functionc                 C      |  |dS )NrY  r  rM   r>   r>   r?   _print_euler:
  rF   zPrettyPrinter._print_eulerc                 C   r  )Nr  r  rM   r>   r>   r?   _print_catalan=
  rF   zPrettyPrinter._print_catalanc                 C   r  )Nr  r  rM   r>   r>   r?   _print_bernoulli@
  rF   zPrettyPrinter._print_bernoullic                 C   r  )NLr  rM   r>   r>   r?   _print_lucasE
  rF   zPrettyPrinter._print_lucasc                 C   r  )Nrp  r  rM   r>   r>   r?   _print_fibonacciH
  rF   zPrettyPrinter._print_fibonaccic                 C   r  )Nr  r  rM   r>   r>   r?   _print_tribonacciK
  rF   zPrettyPrinter._print_tribonaccic                 C   s   | j r	| |dS | |dS )Nu   γ	stieltjes)rH   r  rM   r>   r>   r?   _print_stieltjesN
  s   zPrettyPrinter._print_stieltjesc                 C   s   |  |jd }t|td }t||  |jd  }| jr(ttd}ntd}|}t|d|   }t|d|   }t|	|dtj
iS )Nr   r   r_   r  r   r   r   )rI   rS   r   ri   rH   r   r   rU   r   r   POW)r<   rN   rW   r  ro  r?  r@  r>   r>   r?   _print_KroneckerDeltaT
  s   z#PrettyPrinter._print_KroneckerDeltac                 C   s   t |dr| d}t|| |  }|S t |drD| d}t|| |j }t|| d }t|| |j }|S t |dr[| d}t|| |j }|S | d S )N
as_booleanzDomain: rP  z in r  z
Domain on )r  rI   r   ri   r  r  rP  )r<   r   rW   r>   r>   r?   _print_RandomDomaina
  s   






z!PrettyPrinter._print_RandomDomainc                 C   sD   z|j d ur| |j |W S W n	 ty   Y nw | t|S rA   )r  rI   to_sympyr   reprr<   r]  r>   r>   r?   
_print_DMPs
  s   
zPrettyPrinter._print_DMPc                 C   r  rA   )r  r  r>   r>   r?   
_print_DMF|
  r  zPrettyPrinter._print_DMFc                 C      |  t|jS rA   rI   r   rY   )r<   objectr>   r>   r?   _print_Object
  r>  zPrettyPrinter._print_Objectc                 C   s8   t d}| |j}| |j}|||d }t|S )Nz-->r   )r   rI   r  codomainri   r   )r<   morphismr  r  r	  tailr>   r>   r?   _print_Morphism
  s
   zPrettyPrinter._print_Morphismc                 C   s.   |  t|j}| |}t|d|d S )Nr  r   )rI   r   rY   r  r   ri   )r<   r
  r  pretty_morphismr>   r>   r?   _print_NamedMorphism
  s   
z"PrettyPrinter._print_NamedMorphismc                 C   s"   ddl m} | ||j|jdS )Nr   )NamedMorphismid)sympy.categoriesr  r  r  r	  )r<   r
  r  r>   r>   r?   _print_IdentityMorphism
  s   z%PrettyPrinter._print_IdentityMorphismc                 C   sT   t d}dd |jD }|  ||d }| |}| |}t||d S )Nr  c                 S   s   g | ]}t |jqS r>   )r   rY   )ra  	componentr>   r>   r?   rd  
  s    z:PrettyPrinter._print_CompositeMorphism.<locals>.<listcomp>r  r   )r   r  reverser  rI   r  r   ri   )r<   r
  circlecomponent_names_listcomponent_namesr  r  r>   r>   r?   _print_CompositeMorphism
  s   

z&PrettyPrinter._print_CompositeMorphismc                 C   r  rA   r  )r<   categoryr>   r>   r?   _print_Category
  r>  zPrettyPrinter._print_Categoryc                 C   sX   |j s	| tjS | |j }|jr&dtd }| |jd }|||}t|d S )Nr   z==>r   )premisesrI   r   EmptySetconclusionsr   ri   r   )r<   diagrampretty_resultresults_arrowpretty_conclusionsr>   r>   r?   _print_Diagram
  s   zPrettyPrinter._print_Diagramc                    s2   ddl m} | fddt jD }| |S )Nr   )Matrixc                    s&   g | ]  fd dt jD qS )c                    s,   g | ]} |f r |f nt d qS )r   r   )ra  r4   )gridr)   r>   r?   rd  
  s    $z?PrettyPrinter._print_DiagramGrid.<locals>.<listcomp>.<listcomp>)r  r   rV  r$  )r)   r?   rd  
  s
    
z4PrettyPrinter._print_DiagramGrid.<locals>.<listcomp>)r  r#  r  r  rq  )r<   r$  r#  matrixr>   r%  r?   _print_DiagramGrid
  s
   
z PrettyPrinter._print_DiagramGridc                 C   r  r  r  r<   r  r>   r>   r?   _print_FreeModuleElement
  s   z&PrettyPrinter._print_FreeModuleElementc                 C   s   |  |jddS )Nr;  r<  )rR   r  r<   rh  r>   r>   r?   _print_SubModule
  r>  zPrettyPrinter._print_SubModulec                 C   s   |  |j|  |j S rA   )rI   r  r0  r*  r>   r>   r?   _print_FreeModule
  rL   zPrettyPrinter._print_FreeModulec                 C   s   |  dd |jjD ddS )Nc                 S   s   g | ]\}|qS r>   r>   r  r>   r>   r?   rd  
  s    z?PrettyPrinter._print_ModuleImplementedIdeal.<locals>.<listcomp>r;  r<  )rR   _moduler  r*  r>   r>   r?   _print_ModuleImplementedIdeal
  s   z+PrettyPrinter._print_ModuleImplementedIdealc                 C      |  |j|  |j S rA   )rI   r  
base_idealr<   Rr>   r>   r?   _print_QuotientRing
  rL   z!PrettyPrinter._print_QuotientRingc                 C      |  |j|  |jj S rA   )rI   datar  r0  r1  r>   r>   r?   _print_QuotientRingElement
     z(PrettyPrinter._print_QuotientRingElementc                 C   r4  rA   )rI   r5  modulekilled_moduler(  r>   r>   r?   _print_QuotientModuleElement
  r7  z*PrettyPrinter._print_QuotientModuleElementc                 C   r/  rA   )rI   r  r9  r*  r>   r>   r?   _print_QuotientModule
  rL   z#PrettyPrinter._print_QuotientModulec              	   C   sN   |  | }| d |_t|d|  |jdtdd |  |j }|S )Nr   z : z %s> r!  )	rI   _sympy_matrixr  r   r   ri   r  r   r	  )r<   r  r&  rW   r>   r>   r?   _print_MatrixHomomorphism
  s   z'PrettyPrinter._print_MatrixHomomorphismc                 C   r  rA   rI   rY   )r<   manifoldr>   r>   r?   _print_Manifold
  rF   zPrettyPrinter._print_Manifoldc                 C   r  rA   r>  )r<   patchr>   r>   r?   _print_Patch
  rF   zPrettyPrinter._print_Patchc                 C   r  rA   r>  )r<   coordsr>   r>   r?   _print_CoordSystem
  rF   z PrettyPrinter._print_CoordSystemc                 C   s   |j j|j j}| t|S rA   )
_coord_sysr  _indexrY   rI   r   )r<   r  stringr>   r>   r?   _print_BaseScalarField
  s   z$PrettyPrinter._print_BaseScalarFieldc                 C   s*   t dd |jj|j j }| t|S )Nr   r   )r"   rE  r  rF  rY   rI   r   )r<   r  r   r>   r>   r?   _print_BaseVectorField
  s   z$PrettyPrinter._print_BaseVectorFieldc                 C   sj   | j rd}nd}|j}t|dr#|jj|j j}| |d t| S | |}t	|
  }t	|| S )Nu   ⅆr   rE  r   )rH   _form_fieldr  rE  r  rF  rY   rI   r   r   rT   rU   )r<   rz  r   r  rG  rW   r>   r>   r?   _print_Differential
  s   

z!PrettyPrinter._print_Differentialc                 C   s8   |  |jd }t|d|jj  }t|d }|S )Nr   z%s(rd   )rI   rS   r   rU   r   r   ri   )r<   r]  rW   r>   r>   r?   	_print_Tr
  s   zPrettyPrinter._print_Trc                 C   J   |  |jd }t|  }| jrt|td  }|S t|d }|S )Nr   nurI   rS   r   rT   rH   rU   r!   rV   r>   r>   r?   _print_primenu     zPrettyPrinter._print_primenuc                 C   rM  )Nr   OmegarO  rV   r>   r>   r?   _print_primeomega  rQ  zPrettyPrinter._print_primeomegac                 C   s$   |j j dkr| d}|S | |S )Ndegree   °)rY   rI   rE   rV   r>   r>   r?   _print_Quantity  s   

zPrettyPrinter._print_Quantityc                 C   sD   t dt|j d }| |j}| |j}t t||| }|S )Nr   )r   r   r   rI   r   r   r   r   r   r>   r>   r?   _print_AssignmentBase  s
   z#PrettyPrinter._print_AssignmentBasec                 C   r  rA   r>  r  r>   r>   r?   
_print_Str%  rF   zPrettyPrinter._print_StrrA   )F)T)rr  rs  )NNr   F)FNrc   rd   )FNr  Frc   rd   )r   
__module____qualname____doc__printmethod_default_settingsr5   rE   propertyrH   rK   rO   rP   rX   r\   _print_RandomSymbolr^   ra   rm   ru   rx   ry   r}   r   r   _print_Infinity_print_NegativeInfinity_print_EmptySet_print_Naturals_print_Naturals0_print_Integers_print_Rationals_print_Complexes_print_EmptySequencer   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r   r3  r$  rR  r\  rq  rv  r|  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r,  r9  rE  rG  rH  rM  rO  rP  rS  r^  rc  rd  rk  rx  r  r  r  r   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r4  r<  r=  rC  rE  rI  rT  rV  rb  rg  ri  ro  rs  rv  rw  r  r  r  r  r  r  r  r  _print_SeqPer_print_SeqAdd_print_SeqMulrR   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  _print_bellr  r  r  r  r  r  r  r  r  r  r  r  r  r  r"  r'  r)  r+  r,  r.  r3  r6  r:  r;  r=  r@  rB  rD  rH  rI  rK  rL  rP  rS  rV  rW  rX  r>   r>   r>   r?   r%      s   
					%%K6aE		

$f!# 8	0T%

		H=,			)
						r%   c                 K   s:   t |}|jd }t|}z
|| W t| S t| w )zReturns a string containing the prettified form of expr.

    For information on keyword arguments see pretty_print function.

    r,   )r%   r7   r    rK   )rD   r=   r  r,   uflagr>   r>   r?   r  )  s   

r  c                 K   s   t t| fi | dS )a  Prints expr in pretty form.

    pprint is just a shortcut for this function.

    Parameters
    ==========

    expr : expression
        The expression to print.

    wrap_line : bool, optional (default=True)
        Line wrapping enabled/disabled.

    num_columns : int or None, optional (default=None)
        Number of columns before line breaking (default to None which reads
        the terminal width), useful when using SymPy without terminal.

    use_unicode : bool or None, optional (default=None)
        Use unicode characters, such as the Greek letter pi instead of
        the string pi.

    full_prec : bool or string, optional (default="auto")
        Use full precision.

    order : bool or string, optional (default=None)
        Set to 'none' for long expressions if slow; default is None.

    use_unicode_sqrt_char : bool, optional (default=True)
        Use compact single-character square root symbol (when unambiguous).

    root_notation : bool, optional (default=True)
        Set to 'False' for printing exponents of the form 1/n in fractional form.
        By default exponent is printed in root form.

    mat_symbol_style : string, optional (default="plain")
        Set to "bold" for printing MatrixSymbols using a bold mathematical symbol face.
        By default the standard face is used.

    imaginary_unit : string, optional (default="i")
        Letter to use for imaginary unit when use_unicode is True.
        Can be "i" (default) or "j".
    N)printr  )rD   kwargsr>   r>   r?   pretty_print<  s   +rp  c                 K   sH   ddl m} ddlm} d|vrd|d< |t| fi ||  dS )a  Prints expr using the pager, in pretty form.

    This invokes a pager command using pydoc. Lines are not wrapped
    automatically. This routine is meant to be used with a pager that allows
    sideways scrolling, like ``less -S``.

    Parameters are the same as for ``pretty_print``. If you wish to wrap lines,
    pass ``num_columns=None`` to auto-detect the width of the terminal.

    r   )pager)getpreferredencodingr.   i  N)pydocrq  localerr  r  encode)rD   r=   rq  rr  r>   r>   r?   pager_printl  s
    rv  );r1  
sympy.corer   sympy.core.addr   sympy.core.containersr   sympy.core.functionr   sympy.core.mulr   sympy.core.numbersr   r	   sympy.core.powerr
   sympy.core.sortingr   sympy.core.symbolr   sympy.core.sympifyr   sympy.printing.conventionsr   sympy.printing.precedencer   r   r   sympy.printing.printerr   r   sympy.printing.strr   sympy.utilities.iterablesr   sympy.utilities.exceptionsr    sympy.printing.pretty.stringpictr   r   &sympy.printing.pretty.pretty_symbologyr   r   r   r   r   r   r    r!   r"   r#   r$   pprint_use_unicodepprint_try_use_unicoder%   r  rp  pprintrv  r>   r>   r>   r?   <module>   sb    4                      !
-