o o hn@sddlmZddlmZddlmZddlmZddlm Z ddl m Z ddl m Z mZmZmZdd lmZd d Zd d ZddZddZdS)) defaultdictAdd)Mul)S)construct_domain)PolyNonlinearError)SDM sdm_irrefsdm_particular_from_rrefsdm_nullspace_from_rref) filldedentcCsFt|}t||\}}t|||}|j}|js|jr$|d}t |\}}} |r5|d|kr5dSt ||d|} t ||j ||| \} } t t} | D]\}}| ||||qPt| | D]\}}||}|D]\}}| |||||qrqfdd| D} tj}t|t| D]}|| |<q| S)aSolve a linear system of equations. Examples ======== Solve a linear system with a unique solution: >>> from sympy import symbols, Eq >>> from sympy.polys.matrices.linsolve import _linsolve >>> x, y = symbols('x, y') >>> eqs = [Eq(x + y, 1), Eq(x - y, 2)] >>> _linsolve(eqs, [x, y]) {x: 3/2, y: -1/2} In the case of underdetermined systems the solution will be expressed in terms of the unknown symbols that are unconstrained: >>> _linsolve([Eq(x + y, 0)], [x, y]) {x: -y, y: y} rNr cSi|] \}}|t|qSr).0stermsrrq/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/polys/matrices/linsolve.py mz_linsolve..)len_linear_eq_to_dictsympy_dict_to_dmdomain is_RealFieldis_ComplexFieldto_ddmrrefto_sdmr r r onerlistitemsappendto_sympyziprZeroset)eqssymsnsymseqsdictconstAaugKArrefpivotsnzcolsPV nonpivotssolivnpiVisymzerorrrr _linsolve0s0   r=c st|jdd|D}t|ddd\}}tt||t|}t|}tt|t|g}t||D] \} } fdd| D} | rM|  | |<| rT|| q4t t |||df|} | S)z?Convert a system of dict equations to a sparse augmented matrixcss|]}|VqdS)N)values)rerrr zsz#sympy_dict_to_dm..T)field extensioncsi|] \}}||qSrr)rrcelem_map sym2indexrrrsz$sympy_dict_to_dm..r ) r(unionrdictr&rranger#r$r enumerate) eqs_coeffseqs_rhsr*elemsr/elems_Kneqsr+r,eqrhseqdictsdm_augrrDrrxs  rcCsg}g}t|}|D]T}|jrMt|j|\}}t|j|\}} ||8}| D]\} } | |vr8|| | 8<q'| || <q'dd|D}||} } nt||\} } || || q ||fS)amConvert a system Expr/Eq equations into dict form, returning the coefficient dictionaries and a list of syms-independent terms from each expression in ``eqs```. Examples ======== >>> from sympy.polys.matrices.linsolve import _linear_eq_to_dict >>> from sympy.abc import x >>> _linear_eq_to_dict([2*x + 3], {x}) ([{x: 2}], [3]) cSsi|] \}}|r||qSrr)rkr8rrrrrz&_linear_eq_to_dict..)r( is_Equality _lin_eq2dictlhsrQr#r$)r)r*coeffsindsymsetr?coeffrcRtRrTr8rCdrrrrs$     rc sF||vr tj|tjifS|jrHtt}g}|jD]}t||\}}||| D] \}}|||q*qt |dd| D} | fS|j rd} } g}|jD]!}t||\}}|se||qT| durn|} |} qTt t d|t|| durifSfdd| D} | | fS||s|ifSt d|)areturn (c, d) where c is the sym-independent part of ``a`` and ``d`` is an efficiently calculated dictionary mapping symbols to their coefficients. A PolyNonlinearError is raised if non-linearity is detected. The values in the dictionary will be non-zero. Examples ======== >>> from sympy.polys.matrices.linsolve import _lin_eq2dict >>> from sympy.abc import x, y >>> _lin_eq2dict(x + 2*y + 3, {x, y}) (3, {x: 1, y: 2}) cSrrr)rr;rXrrrrrz _lin_eq2dict..Nz- nonlinear cross-term: %scsi|] \}}||qSrr)rr;rCr[rrrrznonlinear term: %s)rr'Oneis_Addrr"argsrVr$r#ris_Mulrrr _from_args has_xfree) arZ terms_list coeff_listaicitimijcijr terms_coeffrr_rrVsF        rVN) collectionsrsympy.core.addrsympy.core.mulrsympy.core.singletonrsympy.polys.constructorrsympy.polys.solversrsdmr r r r sympy.utilities.miscrr=rrrVrrrrs       H &