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equation.c File ReferenceImplementation of the functions operating on Tequation. More... #include "equation.h" #include "defines.h" #include <string.h> #include <math.h> Go to the source code of this file.
Detailed DescriptionImplementation of the functions operating on Tequation.
Definition in file equation.c. Function Documentation
Removes the information about monomials stored in the equation.
Definition at line 35 of file equation.c. References DeleteMonomial(), Tequation::monomials, and Tequation::nMonomials. Referenced by DeleteEquation(), and ResetEquation().
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Monomials with a constant value below ZERO are removed.
Definition at line 49 of file equation.c. References AddMonomial(), Tequation::cmp, CopyEquation(), DeleteEquation(), GetMonomialCt(), InitEquation(), Tequation::monomials, Tequation::nMonomials, Tequation::type, Tequation::value, and ZERO. Referenced by AccumulateEquations(), NormalizeEquation(), and RewriteEquation().
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Creates an empty equation.
Definition at line 73 of file equation.c. References Tequation::cmp, INIT_NUM_MONOMIALS, InitVarSet(), Tequation::maxMonomials, Tequation::monomials, NEW, Tequation::nMonomials, NOCMP, NOTYPE_EQ, Tequation::order, Tequation::type, Tequation::value, and Tequation::vars. Referenced by AddTerm2SearchCriterion(), DummifyAndAddEquation(), EquationFromLinearConstraint(), EquationFromLinearConstraintProduct(), GenerateCrossProductEquations(), GenerateDotProductEquation(), GenerateGeneralNormEquation(), GenerateJointEquations(), GenerateJointRangeEquations(), GenerateScaledParabolaEquation(), GenerateScaledSaddleEquation(), GenerateTransEquationsFromBranch(), InitCuikSystem(), PurgeEquation(), ReplaceVariableInEquation(), and RewriteEquation().
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Defines a new equation from a linear constraint. Only linear constraint with a constant right-hand term can be converted to equations. For other linear constraints this funtion triggers an error.
Definition at line 92 of file equation.c. References AddCt2Monomial(), AddMonomial(), AddVariable2Monomial(), Tequation::cmp, DeleteMonomial(), EQU, Error(), GEQ, GetLinearConstraintCoefficient(), GetLinearConstraintError(), GetLinearConstraintVariable(), GetNumTermsInLinearConstraint(), INF, InitEquation(), InitMonomial(), IntervalCenter(), IntervalSize(), LEQ, LowerLimit(), UpperLimit(), and Tequation::value. Referenced by RewriteEquation().
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Defines a new equation from the product of two linear constraint. Only linear constraint with a constant right-hand term are considered. For other linear constraints this funtion triggers an error.
Definition at line 142 of file equation.c. References AddCt2Monomial(), AddMonomial(), AddVariable2Monomial(), DeleteMonomial(), Error(), GetLinearConstraintCoefficient(), GetLinearConstraintError(), GetLinearConstraintVariable(), GetNumTermsInLinearConstraint(), InitEquation(), InitMonomial(), IntervalCenter(), and IntervalSize(). Referenced by RewriteEquation().
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Creates one equation copying the information from another equation.
Definition at line 202 of file equation.c. References AddMonomial(), Tequation::cmp, InitVarSet(), Tequation::maxMonomials, Tequation::monomials, NEW, Tequation::nMonomials, Tequation::order, Tequation::type, Tequation::value, and Tequation::vars. Referenced by CopyCuikSystem(), CopyEquationInfo(), CuikSystemMerge(), GaussianElimination(), GetCSEquation(), PurgeEquation(), ReplaceVariableInEquation(), SetCSSearchMode(), and SetEquationInfo().
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Transform an equation expressed in a given set of variables into an equation in the simplified set of variables. The relation between the two sets of variables is given by a mapping.
Definition at line 221 of file equation.c. References AccumulateEquations(), AddMonomial(), Tequation::cmp, DeleteEquation(), DeleteLinearConstraint(), EquationFromLinearConstraint(), EquationFromLinearConstraintProduct(), Error(), GetMonomialCt(), GetMonomialVariables(), GetOriginalVarRelation(), GetVariableN(), InitEquation(), MonomialOrder(), Tequation::monomials, Tequation::nMonomials, PurgeEquation(), Tequation::type, Tequation::value, and VariableSetSize(). Referenced by UpdateCuikSystem().
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Adds a scaled equation to another equation.
Definition at line 290 of file equation.c. References AddCt2Monomial(), AddMonomial(), CopyMonomial(), DeleteMonomial(), Tequation::monomials, Tequation::nMonomials, PurgeEquation(), and Tequation::value. Referenced by AddTerm2SearchCriterion(), CuikSystemMerge(), GaussianElimination(), and RewriteEquation().
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Removes the information stored in the equation, but does not frees the memory. It is more efficient to use ResetEquation instead of DeleteEquation plus InitEquation again.
Definition at line 306 of file equation.c. References Tequation::cmp, NOCMP, NOTYPE_EQ, Tequation::order, ResetEquationMonomials(), ResetVarSet(), Tequation::type, Tequation::value, and Tequation::vars. Referenced by UpdateCuikSystem().
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Removes a variable from an equation converting it into a constant. Note, that variables are indexed and that removing a variable shifts down the index of variables with index above the removed variable.
Definition at line 324 of file equation.c. References AddCt2LinearConstraint(), DeleteLinearConstraint(), InitLinearConstraint(), and ReplaceVariableInEquation(). Referenced by RemoveEquationsWithVar().
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Replaces a variable from an equation converting it to a linear combination of variables. Note, that variables are indexed and that removing a variable shifts down the index of variables with index above the removed variable.
Definition at line 344 of file equation.c. References AddCt2Monomial(), AddMonomial(), AddVariable2Monomial(), Tequation::cmp, CopyEquation(), CopyMonomial(), DeleteEquation(), DeleteMonomial(), EQU, Error(), FixVariableInMonomial(), GEQ, GetEquationCmp(), GetEquationType(), GetEquationValue(), GetLinearConstraintCoefficient(), GetLinearConstraintError(), GetLinearConstraintVariable(), GetMonomialVariables(), GetNumTermsInLinearConstraint(), GetPlaceinSet(), GetVariablePowerN(), InitEquation(), IntervalCenter(), IntervalSize(), LEQ, Tequation::monomials, Tequation::nMonomials, NO_UINT, NormalizeEquation(), SetEquationCmp(), SetEquationType(), SetEquationValue(), ShiftVarIndexes(), TRUE, Tequation::value, VariableSetSize(), and ZERO. Referenced by FixVariableInEquation(), and ReplaceVariableInEquations().
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Scales the equation by a constant factor. Only equalities are scaled and if the scale factor is 0 this function triggers an error.
Definition at line 485 of file equation.c. References AddCt2Monomial(), Tequation::cmp, EQU, Error(), Tequation::monomials, Tequation::nMonomials, Tequation::value, and ZERO.
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Scales the equation by a variable factor. Only equalities are scaled.
Definition at line 502 of file equation.c. References AddCt2Monomial(), AddMonomial(), AddVariable2Monomial(), Tequation::cmp, DeleteMonomial(), EQU, Error(), GetMonomialVariables(), InitMonomial(), Tequation::monomials, Tequation::nMonomials, ResetVarSet(), UnionVarSet(), Tequation::value, and Tequation::vars.
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Simple form of normalization to avoid numerical inestabilities. If all monomials have the same ct (up to ZERO) we make them all equal to one. This helps in many cases when we replace variables to avoid transforming, for instance, a circle equation into a scaled circle equation (that is not identified as a circle!)
Definition at line 536 of file equation.c. References AddCt2Monomial(), Tequation::cmp, EQU, GetMonomialCt(), Tequation::monomials, Tequation::nMonomials, PurgeEquation(), SetMonomialCt(), TRUE, Tequation::value, and ZERO. Referenced by AddEquation(), and ReplaceVariableInEquation().
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Checks if a given variable can be remove from the system and replaced by a linear combination of the surving variables. The output variables (v and lc) are only initilized if some simplification is possible (i.e., if the return is TRUE).
Definition at line 585 of file equation.c. References AddCt2LinearConstraint(), AddTerm2LinearConstraint(), Tequation::cmp, EQU, FALSE, GetEquationOrder(), GetMonomialCt(), GetMonomialVariables(), GetVariableN(), INF, InitLinearConstraint(), InvertLinearConstraint(), MAX_TERMS_SIMP, Tequation::monomials, Tequation::nMonomials, NO_UINT, ScaleLinearConstraint(), TRUE, Tequation::value, VariableSetSize(), and Tequation::vars. Referenced by CSRemoveLCVars().
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Sets a new type for the equation.
Definition at line 727 of file equation.c. References Tequation::type. Referenced by DummifyAndAddEquation(), GenerateCrossProductEquations(), GenerateDotProductEquation(), GenerateGeneralNormEquation(), GenerateJointEquations(), GenerateJointRangeEquations(), GenerateScaledParabolaEquation(), GenerateScaledSaddleEquation(), GenerateTransEquationsFromBranch(), and ReplaceVariableInEquation().
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Sets a new relational operator for the equation.
Definition at line 732 of file equation.c. References Tequation::cmp, EQU, Error(), GEQ, and LEQ. Referenced by AddTerm2SearchCriterion(), DummifyAndAddEquation(), GenerateCrossProductEquations(), GenerateDotProductEquation(), GenerateGeneralNormEquation(), GenerateJointEquations(), GenerateJointRangeEquations(), GenerateScaledParabolaEquation(), GenerateScaledSaddleEquation(), GenerateTransEquationsFromBranch(), and ReplaceVariableInEquation().
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Sets a new rigth-hand value for the equation.
Definition at line 740 of file equation.c. References Tequation::value. Referenced by DummifyAndAddEquation(), GenerateCrossProductEquations(), GenerateDotProductEquation(), GenerateGeneralNormEquation(), GenerateJointRangeEquations(), GenerateScaledParabolaEquation(), GenerateScaledSaddleEquation(), and ReplaceVariableInEquation().
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Identify linear equations.
Definition at line 745 of file equation.c. References CtMonomial(), LinearMonomial(), Tequation::monomials, and TRUE. Referenced by DummifyAndAddEquation(), and SetEquationInfo().
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Identify bilinear equations.
Definition at line 758 of file equation.c. References BilinearMonomial(), CtMonomial(), LinearMonomial(), Tequation::monomials, QuadraticMonomial(), and TRUE.
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Identify circle equations.
Definition at line 777 of file equation.c. References FALSE, GetMonomialCt(), Tequation::monomials, Tequation::nMonomials, QuadraticMonomial(), TRUE, and Tequation::value. Referenced by DummifyAndAddEquation(), and SetEquationInfo().
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Identify sphere equations.
Definition at line 792 of file equation.c. References Tequation::cmp, EQU, FALSE, GetMonomialCt(), Tequation::monomials, Tequation::nMonomials, QuadraticMonomial(), TRUE, and Tequation::value. Referenced by DummifyAndAddEquation(), and SetEquationInfo().
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Identify scaled saddle equations, i.e., equations of the form .
Definition at line 807 of file equation.c. References BilinearMonomial(), Tequation::cmp, EQU, FALSE, GetMonomialCt(), LinearMonomial(), Tequation::monomials, Tequation::nMonomials, TRUE, and Tequation::value. Referenced by DummifyAndAddEquation(), and SetEquationInfo().
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Identify parabola equations, i.e., equations of the form .
Definition at line 821 of file equation.c. References Tequation::cmp, EQU, FALSE, GetMonomialCt(), LinearMonomial(), Tequation::monomials, Tequation::nMonomials, QuadraticMonomial(), TRUE, and Tequation::value. Referenced by DummifyAndAddEquation(), and SetEquationInfo().
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Gets the type of relational operator of the equation.
Definition at line 835 of file equation.c. References Tequation::cmp. Referenced by AddEquation(), AddEquation2Simplex(), ComputeSimpCuikSystemJacobian(), CoordInequalitiesHold(), CropEquation(), DummifyAndAddEquation(), ErrorInInequalities(), ErrorInSolution(), GaussianElimination(), LinearizeCircleEquation(), LinearizeGeneralEquation(), ReplaceVariableInEquation(), and SetEquationInfo().
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Gets the equation type.
Definition at line 840 of file equation.c. References Tequation::type. Referenced by AddEquation(), CoordInequalitiesHold(), DummifyAndAddEquation(), ErrorInSolution(), GaussianElimination(), GetEquationTypeN(), IsCoordEquation(), IsDummyEquation(), IsSystemEquation(), ReplaceVariableInEquation(), and UsedVarInNonDummyEquations().
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Gets the right-hand value of the equation.
Definition at line 845 of file equation.c. References Tequation::value. Referenced by AddEquation2Simplex(), CoordInequalitiesHold(), CropEquation(), DummifyAndAddEquation(), ErrorInInequalities(), ErrorInSolution(), EvaluateEqMin(), GetFirstOrderApproximationToEquation(), LinearizeCircleEquation(), LinearizeSphereEquation(), MoveWorld(), ReplaceVariableInEquation(), and SetEquationInfo().
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Gets the equation order: 1 for lineal, 2 for bilinear and quadratic.
Definition at line 850 of file equation.c. References Tequation::order. Referenced by CmpEquations(), IsSimplificable(), and LinearEquation2LinearConstraint().
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Gets the set of variables equation used in the equation. Note, we return a pointer to the interval equation structures so be careful what you do with the pointer.
Definition at line 855 of file equation.c. References Tequation::vars. Referenced by AddEquation2Simplex(), CropEquation(), DummifyAndAddEquation(), ErrorDueToVariable(), GetEquationNumVariables(), GetFirstOrderApproximationToEquation(), LinearizeCircleEquation(), LinearizeGeneralEquation(), LinearizeGeneralEquationInt(), LinearizeSphereEquation(), RemoveEquationsWithVar(), SetEquationInfo(), UpdateSplitWeight(), UsedVarInEquations(), and UsedVarInNonDummyEquations().
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Gets the number of variables equation used in the equation.
Definition at line 860 of file equation.c. References GetEquationVariables(), and VariableSetSize(). Referenced by GaussianElimination().
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Returns 1 if eq1<eq2, 0 if eq1=eq2 or 2 if eq1>eq2. Equations are sorted according to
Definition at line 865 of file equation.c. References Tequation::cmp, CmpMonomial(), GetEquationOrder(), Tequation::monomials, Tequation::nMonomials, Tequation::type, and Tequation::value. Referenced by AddEquation(), and HasEquation().
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Adds a new monomial to the equation.
Definition at line 932 of file equation.c. References CmpMonomial(), CopyMonomial(), CtMonomial(), DeleteMonomial(), EmptyMonomial(), Error(), FindMonomial(), GetMonomialCt(), GetMonomialVariables(), Tequation::maxMonomials, MEM_DUP, MonomialOrder(), Tequation::monomials, NEW, Tequation::nMonomials, NO_UINT, Tequation::order, ResetVarSet(), SetMonomialCt(), UnionVarSet(), Tequation::value, Tequation::vars, and ZERO. Referenced by AccumulateEquations(), AddTerm2SearchCriterion(), ApplyLinkRot(), CopyEquation(), DeriveEquation(), DummifyAndAddEquation(), EquationFromLinearConstraint(), EquationFromLinearConstraintProduct(), GenerateCrossProductEquations(), GenerateDotProductEquation(), GenerateEquationsFromBranch(), GenerateGeneralNormEquation(), GenerateJointEquations(), GenerateJointEquationsInBranch(), GenerateJointRangeEquations(), GenerateScaledParabolaEquation(), GenerateScaledSaddleEquation(), PurgeEquation(), ReplaceVariableInEquation(), RewriteEquation(), and VarScaleEquation().
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Generates a parabola equation vx^2-vy=0.
Definition at line 1010 of file equation.c. References GenerateScaledParabolaEquation().
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Generates a parabola equation s*vx^2-vy=0.
Definition at line 1015 of file equation.c. References AddCt2Monomial(), AddMonomial(), AddVariable2Monomial(), DeleteMonomial(), DUMMY_EQ, EQU, Error(), InitEquation(), InitMonomial(), ResetMonomial(), SetEquationCmp(), SetEquationType(), and SetEquationValue(). Referenced by GenerateParabolaEquation(), and GenerateScaledSaddleEquation().
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Generates a saddle equation vx*vy-vz=0. If vx is the same as vy a parabola equation is generated.
Definition at line 1041 of file equation.c. References GenerateScaledSaddleEquation(). Referenced by GenerateJointEquations().
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Generates a saddle equation s*vx*vy-vz=0. If vx is the same as vy a scaled parabola equation is generated.
Definition at line 1047 of file equation.c. References AddCt2Monomial(), AddMonomial(), AddVariable2Monomial(), DeleteMonomial(), DUMMY_EQ, EQU, Error(), GenerateScaledParabolaEquation(), InitEquation(), InitMonomial(), ResetMonomial(), SetEquationCmp(), SetEquationType(), and SetEquationValue(). Referenced by GenerateSaddleEquation().
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This is a special case of GenerateGeneralNormEquation where the vector has only 3 variables.
Definition at line 1080 of file equation.c. References GenerateGeneralNormEquation(). Referenced by GenerateJointEquations(), and GenerateLinkRot().
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Generates an equation that is the norm of a vector with nv variables n. Thus, the equation created is
Definition at line 1092 of file equation.c. References AddMonomial(), AddVariable2Monomial(), DeleteMonomial(), EQU, InitEquation(), InitMonomial(), ResetMonomial(), SetEquationCmp(), SetEquationType(), SetEquationValue(), and SYSTEM_EQ. Referenced by GenerateNormEquation().
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Generates the three equations of the cross product of two unitary vectors that give as a result a third vector (orthogonal to the two operated vectors) scaled by the sinus of the angle between these two vectors.
Definition at line 1113 of file equation.c. References AddCt2Monomial(), AddMonomial(), AddVariable2Monomial(), DeleteMonomial(), EQU, InitEquation(), InitMonomial(), NO_UINT, ResetMonomial(), SetEquationCmp(), SetEquationType(), SetEquationValue(), and SYSTEM_EQ. Referenced by GenerateLinkRot().
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Generates the equation corresponding to the dot product of two unitary vectors that give as a result the cosinus of the angle between these two vectors.
Definition at line 1175 of file equation.c. References AddCt2Monomial(), AddMonomial(), AddVariable2Monomial(), DeleteMonomial(), EQU, InitEquation(), InitMonomial(), NO_UINT, ResetMonomial(), SetEquationCmp(), SetEquationType(), SetEquationValue(), and SYSTEM_EQ. Referenced by GenerateJointEquations(), GenerateJointRangeEquations(), and GenerateLinkRot().
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Searches for a given monomial in the equation.
Definition at line 1210 of file equation.c. References CmpVarSet(), FALSE, GetMonomialVariables(), Tequation::monomials, NO_UINT, and TRUE. Referenced by AddMonomial(), and GaussianElimination().
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Gets a monomial from an equation.
Definition at line 1233 of file equation.c. References Tequation::monomials. Referenced by CropEquation(), DummifyAndAddEquation(), GaussianElimination(), LinearizeParabolaEquation(), LinearizeSaddleEquation(), and SetEquationInfo().
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Returns the number of monomials in an equation.
Definition at line 1241 of file equation.c. References Tequation::nMonomials. Referenced by AddEquation(), CropEquation(), DummifyAndAddEquation(), GaussianElimination(), SetEquationInfo(), and UpdateCuikSystem().
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Converts a linear equation into a linear constraint. A linear constraint is just a particular case of equation. We implemented the linear constraints as a different type just for convenience (i.e., to facilitate the simplex implementation). If the input equation is not linear, the output is empty. To approximate a general equation with a linear constraint use GetFirstOrderApproximationToEquation.
Definition at line 1246 of file equation.c. References AddCt2LinearConstraint(), AddTerm2LinearConstraint(), GetEquationOrder(), GetMonomialCt(), GetMonomialVariables(), GetVariableN(), InitLinearConstraint(), Tequation::monomials, Tequation::nMonomials, and Tequation::value.
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Evaluates an equation in a given point. NOTE: The right-hand side value of the equation is not used in the evaluation.
Definition at line 1264 of file equation.c. References Tequation::cmp, Error(), EvaluateMonomial(), Tequation::monomials, Tequation::nMonomials, and NOCMP. Referenced by ErrorInInequalities(), ErrorInSolution(), EvaluateEqMin(), and MoveWorld().
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Evaluates an equation for a given ranges of the variables using interval arithmetics.
Definition at line 1280 of file equation.c. References Tequation::cmp, Error(), EvaluateMonomialInt(), IntervalAdd(), Tequation::monomials, NewInterval(), Tequation::nMonomials, and NOCMP. Referenced by AddEquation2Simplex(), CoordInequalitiesHold(), EvaluateEqMin(), and GetFirstOrderApproximationToEquation().
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Derives an equation with respect to a given variable.
Definition at line 1296 of file equation.c. References AddMonomial(), Tequation::cmp, DeleteMonomial(), DERIVED_EQ, DeriveMonomial(), EQU, InitVarSet(), Tequation::maxMonomials, Tequation::monomials, NEW, Tequation::nMonomials, Tequation::order, Tequation::type, Tequation::value, and Tequation::vars. Referenced by ComputeSimpCuikSystemJacobian(), GetCuikSystemJacobian(), and SetEquationInfo().
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Writes an equation to a given stream as a sequence of monomials, i.e., without the equality and with the right-hand side at the left side. This only works if the equation is a equality. Inequalities are always printed as a normal equations
Definition at line 1322 of file equation.c. References Tequation::cmp, EQU, Tequation::monomials, Tequation::nMonomials, PrintEquation(), PrintMonomial(), Tequation::value, and ZERO. Referenced by PrintCuikSystem(), and PrintCuikSystemWithSimplification().
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Writes an equation to a given stream.
Definition at line 1339 of file equation.c. References Tequation::cmp, EQU, Error(), GEQ, LEQ, Tequation::monomials, Tequation::nMonomials, NOCMP, PrintMonomial(), and Tequation::value. Referenced by AddEquation2Simplex(), CropEquation(), PrintEquations(), and PrintMonomials().
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Deletes the information stored in the equation and frees the allocated memory space.
Definition at line 1365 of file equation.c. References DeleteVarSet(), Tequation::monomials, ResetEquationMonomials(), and Tequation::vars. Referenced by AddTerm2SearchCriterion(), DeleteCuikSystemJacobian(), DeleteEquationInfo(), DeleteSimpCuikSystemJacobian(), DeleteWorld(), DummifyAndAddEquation(), GaussianElimination(), GenerateEquationsFromBranch(), GenerateJointEquations(), GenerateJointRangeEquations(), GenerateLinkRot(), PurgeEquation(), ReplaceVariableInEquation(), RewriteEquation(), SetCSSearchMode(), SetEquationInfo(), and UnUpdateCuikSystem().
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