o o hE@srddlmZddlmZddlmZddlmZddlm Z m Z ddl m Z ddl mZddlmZdd lmZdd lmZdd lmZdd lmZmZmZmZdd lmZddlm Z m!Z!m"Z"GdddeZ#Gddde#e Z$Gdddee#Z%Gdddee#Z&Gdddee#Z'Gddde#Z(Gddde Z)ddZ*dd Z+e#e#_,e&e#_-e%e#_.e'e#_/e$e#_0e'e#_1d!S)") annotations)product)Add) StdFactKB) AtomicExprExpr)Pow)S)default_sort_key)sympifysqrt)ImmutableDenseMatrix)BasisDependentZeroBasisDependentBasisDependentMulBasisDependentAdd) CoordSys3D)Dyadic BaseDyadic DyadicAddc@seZdZUdZdZdZdZded<ded<ded<ded <ded <d ed <ed dZ ddZ ddZ ddZ ddZ e je _ddZddZeje_ddZd*ddZedd Zd!d"Zeje_d#d$Zd%d&Zd'd(Zd)S)+Vectorz Super class for all Vector classes. Ideally, neither this class nor any of its subclasses should be instantiated by the user. FTg(@z type[Vector] _expr_type _mul_func _add_func _zero_func _base_func VectorZerozerocC|jS)a Returns the components of this vector in the form of a Python dictionary mapping BaseVector instances to the corresponding measure numbers. Examples ======== >>> from sympy.vector import CoordSys3D >>> C = CoordSys3D('C') >>> v = 3*C.i + 4*C.j + 5*C.k >>> v.components {C.i: 3, C.j: 4, C.k: 5} ) _componentsselfr#g/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/vector/vector.py components%szVector.componentscCs t||@S)z7 Returns the magnitude of this vector. r r!r#r#r$ magnitude: zVector.magnitudecCs ||S)z@ Returns the normalized version of this vector. )r&r!r#r#r$ normalize@r'zVector.normalizecst|tr/ttr tjStj}|jD]\}}|jd}||||jd7}q|Sddl m }t||tfsFt t |ddt||rSfdd}|St|S)aN Returns the dot product of this Vector, either with another Vector, or a Dyadic, or a Del operator. If 'other' is a Vector, returns the dot product scalar (SymPy expression). If 'other' is a Dyadic, the dot product is returned as a Vector. If 'other' is an instance of Del, returns the directional derivative operator as a Python function. If this function is applied to a scalar expression, it returns the directional derivative of the scalar field wrt this Vector. Parameters ========== other: Vector/Dyadic/Del The Vector or Dyadic we are dotting with, or a Del operator . Examples ======== >>> from sympy.vector import CoordSys3D, Del >>> C = CoordSys3D('C') >>> delop = Del() >>> C.i.dot(C.j) 0 >>> C.i & C.i 1 >>> v = 3*C.i + 4*C.j + 5*C.k >>> v.dot(C.k) 5 >>> (C.i & delop)(C.x*C.y*C.z) C.y*C.z >>> d = C.i.outer(C.i) >>> C.i.dot(d) C.i r)Delz is not a vector, dyadic or z del operatorcsddlm}||S)Nr)directional_derivative)sympy.vector.functionsr+)fieldr+r!r#r$r+}s  z*Vector.dot..directional_derivative) isinstancerrrrr%itemsargsdotsympy.vector.deloperatorr* TypeErrorstr)r"otheroutveckvvect_dotr*r+r#r!r$r1Fs" (      z Vector.dotcC ||SNr1r"r5r#r#r$__and__ zVector.__and__cCsnt|tr2t|tr tjStj}|jD]\}}||jd}||jd}|||7}q|St||S)a Returns the cross product of this Vector with another Vector or Dyadic instance. The cross product is a Vector, if 'other' is a Vector. If 'other' is a Dyadic, this returns a Dyadic instance. Parameters ========== other: Vector/Dyadic The Vector or Dyadic we are crossing with. Examples ======== >>> from sympy.vector import CoordSys3D >>> C = CoordSys3D('C') >>> C.i.cross(C.j) C.k >>> C.i ^ C.i 0 >>> v = 3*C.i + 4*C.j + 5*C.k >>> v ^ C.i 5*C.j + (-4)*C.k >>> d = C.i.outer(C.i) >>> C.j.cross(d) (-1)*(C.k|C.i) rr)) r.rrrr%r/crossr0outer)r"r5outdyadr7r8 cross_productrAr#r#r$r@s  z Vector.crosscCr:r;r@r=r#r#r$__xor__r?zVector.__xor__cCsTt|ts tdt|tst|trtjSddt|j|jD}t |S)a Returns the outer product of this vector with another, in the form of a Dyadic instance. Parameters ========== other : Vector The Vector with respect to which the outer product is to be computed. Examples ======== >>> from sympy.vector import CoordSys3D >>> N = CoordSys3D('N') >>> N.i.outer(N.j) (N.i|N.j) z!Invalid operand for outer productcSs*g|]\\}}\}}||t||qSr#)r).0k1v1k2v2r#r#r$ s*z Vector.outer..) r.rr3rrrrr%r/r)r"r5r0r#r#r$rAs  z Vector.outercCsL|tjr|r tjStjS|r||||S|||||S)a Returns the vector or scalar projection of the 'other' on 'self'. Examples ======== >>> from sympy.vector.coordsysrect import CoordSys3D >>> C = CoordSys3D('C') >>> i, j, k = C.base_vectors() >>> v1 = i + j + k >>> v2 = 3*i + 4*j >>> v1.projection(v2) 7/3*C.i + 7/3*C.j + 7/3*C.k >>> v1.projection(v2, scalar=True) 7/3 )equalsrrr Zeror1)r"r5scalarr#r#r$ projections zVector.projectioncsPddlm}ttrtjtjtjfStt|}t fdd|DS)a Returns the components of this vector but the output includes also zero values components. Examples ======== >>> from sympy.vector import CoordSys3D, Vector >>> C = CoordSys3D('C') >>> v1 = 3*C.i + 4*C.j + 5*C.k >>> v1._projections (3, 4, 5) >>> v2 = C.x*C.y*C.z*C.i >>> v2._projections (C.x*C.y*C.z, 0, 0) >>> v3 = Vector.zero >>> v3._projections (0, 0, 0) r)_get_coord_systemscg|]}|qSr#r<rFir!r#r$rKz'Vector._projections..) sympy.vector.operatorsrPr.rr rMnextiter base_vectorstuple)r"rPbase_vecr#r!r$ _projectionss  zVector._projectionscCr:r;)rAr=r#r#r$__or__r?z Vector.__or__cstfdd|DS)a Returns the matrix form of this vector with respect to the specified coordinate system. Parameters ========== system : CoordSys3D The system wrt which the matrix form is to be computed Examples ======== >>> from sympy.vector import CoordSys3D >>> C = CoordSys3D('C') >>> from sympy.abc import a, b, c >>> v = a*C.i + b*C.j + c*C.k >>> v.to_matrix(C) Matrix([ [a], [b], [c]]) crQr#r<)rFunit_vecr!r#r$rK3rTz$Vector.to_matrix..)MatrixrX)r"systemr#r!r$ to_matrixs zVector.to_matrixcCs:i}|jD]\}}||jtj||||j<q|S)a The constituents of this vector in different coordinate systems, as per its definition. Returns a dict mapping each CoordSys3D to the corresponding constituent Vector. Examples ======== >>> from sympy.vector import CoordSys3D >>> R1 = CoordSys3D('R1') >>> R2 = CoordSys3D('R2') >>> v = R1.i + R2.i >>> v.separate() == {R1: R1.i, R2: R2.i} True )r%r/getr_rr)r"partsvectmeasurer#r#r$separate6s  zVector.separatecCsRt|trt|trtdt|tr%|tjkrtdt|t|tjStd)z( Helper for division involving vectors. zCannot divide two vectorszCannot divide a vector by zeroz#Invalid division involving a vector) r.rr3r rM ValueError VectorMulr NegativeOne)oner5r#r#r$ _div_helperPs  zVector._div_helperN)F)__name__ __module__ __qualname____doc__ is_scalar is_Vector _op_priority__annotations__propertyr%r&r(r1r>r@rErArOr[r\r`rerjr#r#r#r$rs<  >, $  rcsJeZdZdZd fdd ZeddZddZd d Zed d Z Z S) BaseVectorz) Class to denote a base vector. Ncs|dur d|}|durd|}t|}t|}|tddvr%tdt|ts.td|j|}t |t ||}||_ |t j i|_ t j |_|jd||_d||_||_||_||f|_d d i}t||_||_|S) Nzx{}zx_{}rzindex must be 0, 1 or 2zsystem should be a CoordSys3D. commutativeT)formatr4rangerfr.rr3 _vector_namessuper__new__r _base_instanceOner _measure_number_name _pretty_form _latex_form_system_idr _assumptions_sys)clsindexr_ pretty_str latex_strnameobj assumptions __class__r#r$r}bs0        zBaseVector.__new__cCrr;)rr!r#r#r$r_zBaseVector.systemcCrr;)r)r"printerr#r#r$ _sympystrszBaseVector._sympystrcCs"|j\}}||d|j|S)Nrv)r_printr{)r"rrr_r#r#r$ _sympyreprs zBaseVector._sympyreprcCs|hSr;r#r!r#r#r$ free_symbolsrzBaseVector.free_symbols)NN) rkrlrmrnr}rsr_rrr __classcell__r#r#rr$rt\s# rtc@ eZdZdZddZddZdS) VectorAddz2 Class to denote sum of Vector instances. cOtj|g|Ri|}|Sr;)rr}rr0optionsrr#r#r$r}zVectorAdd.__new__c Cszd}t|}|jddd|D]"\}}|}|D]}||jvr5|j||}|||d7}qq|ddS)NrwcSs |dS)Nr)__str__)xr#r#r$s z%VectorAdd._sympystr..keyz + )listrer/sortrXr%r) r"rret_strr/r_rc base_vectsr temp_vectr#r#r$rs   zVectorAdd._sympystrN)rkrlrmrnr}rr#r#r#r$rs rc@s0eZdZdZddZeddZeddZdS) rgz> Class to denote products of scalars and BaseVectors. cOrr;)rr}rr#r#r$r}rzVectorMul.__new__cCr)z) The BaseVector involved in the product. )r~r!r#r#r$ base_vectorszVectorMul.base_vectorcCr)zU The scalar expression involved in the definition of this VectorMul. )rr!r#r#r$measure_numberszVectorMul.measure_numberN)rkrlrmrnr}rsrrr#r#r#r$rgs rgc@s$eZdZdZdZdZdZddZdS)rz' Class to denote a zero vector g333333(@0z\mathbf{\hat{0}}cCst|}|Sr;)rr})rrr#r#r$r}s zVectorZero.__new__N)rkrlrmrnrqrrr}r#r#r#r$rs  rc@r)Crossa Represents unevaluated Cross product. Examples ======== >>> from sympy.vector import CoordSys3D, Cross >>> R = CoordSys3D('R') >>> v1 = R.i + R.j + R.k >>> v2 = R.x * R.i + R.y * R.j + R.z * R.k >>> Cross(v1, v2) Cross(R.i + R.j + R.k, R.x*R.i + R.y*R.j + R.z*R.k) >>> Cross(v1, v2).doit() (-R.y + R.z)*R.i + (R.x - R.z)*R.j + (-R.x + R.y)*R.k cCsJt|}t|}t|t|krt|| St|||}||_||_|Sr;)r r rrr}_expr1_expr2rexpr1expr2rr#r#r$r}s z Cross.__new__cKt|j|jSr;)r@rrr"hintsr#r#r$doitz Cross.doitNrkrlrmrnr}rr#r#r#r$rs rc@r)Dota Represents unevaluated Dot product. Examples ======== >>> from sympy.vector import CoordSys3D, Dot >>> from sympy import symbols >>> R = CoordSys3D('R') >>> a, b, c = symbols('a b c') >>> v1 = R.i + R.j + R.k >>> v2 = a * R.i + b * R.j + c * R.k >>> Dot(v1, v2) Dot(R.i + R.j + R.k, a*R.i + b*R.j + c*R.k) >>> Dot(v1, v2).doit() a + b + c cCsBt|}t|}t||gtd\}}t|||}||_||_|S)Nr)r sortedr rr}rrrr#r#r$r}sz Dot.__new__cKrr;)r1rrrr#r#r$r rzDot.doitNrr#r#r#r$rs rc sttrtfddjDSttr$tfddjDSttrttrjjkrejd}jd}||krEtjShd ||h }|dd|krZdnd}|j |Sdd l m }z|j}WntytYSwt|SttsttrtjSttrttj\}} | t|Sttrttj\} } | t| StS) a^ Returns cross product of two vectors. Examples ======== >>> from sympy.vector import CoordSys3D >>> from sympy.vector.vector import cross >>> R = CoordSys3D('R') >>> v1 = R.i + R.j + R.k >>> v2 = R.x * R.i + R.y * R.j + R.z * R.k >>> cross(v1, v2) (-R.y + R.z)*R.i + (R.x - R.z)*R.j + (-R.x + R.y)*R.k c3|]}t|VqdSr;rDrRvect2r#r$ !zcross..c3|]}t|VqdSr;rDrRvect1r#r$r#rr>rr)r)ruexpress)r.rrfromiterr0rtrrr differencepoprX functionsrrfrr@rrgrVrWr%r/) rrn1n2n3signrr8rHm1rJm2r#rrr$r@s:           r@cs@ttrtfddjDSttr$tfddjDSttr`ttr`jjkr>kr;tjStjSddl m }z|j}Wnt yZt YSwt |SttsjttrmtjSttrttj\}}|t |Sttrttj\}}|t |St S)a2 Returns dot product of two vectors. Examples ======== >>> from sympy.vector import CoordSys3D >>> from sympy.vector.vector import dot >>> R = CoordSys3D('R') >>> v1 = R.i + R.j + R.k >>> v2 = R.x * R.i + R.y * R.j + R.z * R.k >>> dot(v1, v2) R.x + R.y + R.z c3rr;r<rRrr#r$rQrzdot..c3rr;r<rRrr#r$rSrr)r)r.rrr0rtrr rrMrrrfrr1rrgrVrWr%r/)rrrr8rHrrJrr#rr$r1@s.         r1N)2 __future__r itertoolsrsympy.core.addrsympy.core.assumptionsrsympy.core.exprrrsympy.core.powerrsympy.core.singletonr sympy.core.sortingr sympy.core.sympifyr (sympy.functions.elementary.miscellaneousr sympy.matrices.immutablerr^sympy.vector.basisdependentrrrrsympy.vector.coordsysrectrsympy.vector.dyadicrrrrrtrrgrrrr@r1rrrrrrr#r#r#r$s>          K9 !0*