Algebra Tools
Browse all available algebra tools.
Available tools
- Affine Fixed Point Denominator Tool Return only the unique-fixed-point denominator of x↦a*x+b and its degenerate coefficient flag; no affine system is solved.
- Affine Inverse Constant Coefficient Tool Calculate affine inverse constant coefficient from explicit caller-supplied inputs.
- Algebra: Monomial Divisibility Witness Tool Check componentwise monomial divisibility and retain the first exponent coordinate that fails.
- Algebra: Monomial Gcd Exponent Vector Tool Compute the formal monomial GCD exponent vector in a common declared variable order, ignoring coefficients.
- Algebra: Monomial Homogeneous Degree Check Tool Check that every supplied nonzero term monomial has one explicit total degree in a fixed variable dimension; caller omits zero-coefficient terms.
- Algebra: Monomial Lcm Exponent Vector Tool Compute the formal monomial LCM exponent vector in a common declared variable order, ignoring coefficients.
- Algebra: Monomial Multi Degree Label Tool Format an explicit monomial multidegree preserving variable order and zero exponents; no symbolic parser.
- Algebra: Monomial Square Exponent Parity Mask Tool Report odd exponent coordinates and the even-exponent condition for a formal monomial square, without assumptions about coefficients.
- Algebra: Monomial Total Degree Tool Sum nonnegative integer exponents of one explicit monomial; an empty exponent vector denotes a constant.
- Algebra: Monomial Variable Degree Label Tool Read the exponent of one named variable from an explicit unique variable/exponent monomial map, preserving absent-variable zero.
- Algebra: Monomial Variable Partial Term Tool Differentiate one explicit monomial with respect to one variable index; a zero derivative retains the original exponent vector as unused witness.
- Algebra: Monomial Weighted Degree Point Tool Compute one weighted monomial degree from nonnegative integer exponents and positive integer variable weights.
- Algebra: Polynomial Effective Degree Tolerance Tool Determine the effective degree of ascending-power coefficients under an explicit absolute coefficient tolerance, retaining -1 for an all-negligible polynomial; not exact normalization.
- Algebra: Polynomial Horner Stage Tool Evaluate exactly one Horner recurrence stage with explicit prior accumulator; not another full polynomial evaluator.
- Algebra: Polynomial Leading Nonzero Coefficient Tool Extract leading coefficient and degree from ascending-power coefficients using the existing normalization core; zero polynomial has degree -1.
- Algebra: Quadratic Vieta Coefficient Pair Tool Return Vieta sum/product of the two complex roots counted with multiplicity for one explicit nondegenerate quadratic; no root solver.
- Algebraic Fraction Cancellation Exponent Term Tool Compute algebraic fraction cancellation exponent term from explicit bounded inputs.
- Binomial Square Cross Term Tool Calculate binomial square cross term from explicit caller-supplied inputs.
- Complex Conjugate Root Factor Coefficients Tool Compute complex conjugate root factor coefficients from explicit bounded inputs.
- Complex Linear Factor Real Part Tool Form the real quadratic from a complex root and its conjugate.
- Cubic Root Unity Filter Term Tool Calculate cubic root unity filter term from explicit caller-supplied inputs.
- Cubic Vieta Pairwise Root Sum Tool Compute cubic vieta pairwise root sum from explicit bounded inputs.
- Cubic Vieta Root Product Sign Tool Compute cubic vieta root product sign from explicit bounded inputs.
- Depressed Cubic Shift Coordinate Tool Calculate depressed cubic shift coordinate from explicit caller-supplied inputs.
- General Linear System Solver Use bounded partial-pivot Gauss–Jordan elimination to classify a rectangular real linear system and return a particular solution, coefficient nullspace, and reduced augmented matrix under an explicit zero threshold, without a conditioning guarantee.
- Laurent Monomial Inversion Order Tool Calculate laurent monomial inversion order from explicit caller-supplied inputs.
- Linear Equation System Solver Solve a system of two linear equations in two unknowns with Cramer's rule.
- Monic Polynomial Coefficient Scale Tool Calculate monic polynomial coefficient scale from explicit caller-supplied inputs.
- Monomial Absent Variable Indicator Tool Inspect supplied exponents of a nonzero monomial; an unlisted or zero-exponent variable is absent from its support.
- Monomial Lcm Exponent Gap Tool Exponent increments needed to reach the componentwise LCM envelope.
- Monomial Log Magnitude At Point Tool Compute monomial log magnitude at point from explicit bounded inputs.
- Monomial Negative Exponent Denominator Label Tool Compute monomial negative exponent denominator label from explicit bounded inputs.
- Monomial Power Composition Exponent Term Tool Compute monomial power composition exponent term from explicit bounded inputs.
- Monomial Radical Exponent Divisibility Tool Compute monomial radical exponent divisibility from explicit bounded inputs.
- Monomial Sign From Exponent Parities Tool Compute monomial sign from exponent parities from explicit bounded inputs.
- Palindromic Polynomial Middle Index Tool Calculate palindromic polynomial middle index from explicit caller-supplied inputs.
- Polynomial Affine Input Shift Root Coordinate Tool Compute polynomial affine input shift root coordinate from explicit bounded inputs.
- Polynomial Affine Substitution Leading Coefficient Tool Compute polynomial affine substitution leading coefficient from explicit bounded inputs.
- Polynomial Coefficient Binomial Shift Term Tool Compute polynomial coefficient binomial shift term from explicit bounded inputs.
- Polynomial Coefficient Decimal Scale Label Tool Describe the written decimal scale of one polynomial coefficient, preserving trailing fractional zeros and accounting for its explicit exponent.
- Polynomial Complex Conjugate Root Pair Tool Compute polynomial complex conjugate root pair from explicit bounded inputs.
- Polynomial Deflation Leading Pair Tool Calculate polynomial deflation leading pair from explicit caller-supplied inputs.
- Polynomial Derivative Constant Coefficient Tool Compute polynomial derivative constant coefficient from explicit bounded inputs.
- Polynomial Descending Ascending Index Pair Tool Compute polynomial descending ascending index pair from explicit bounded inputs.
- Polynomial Double Root Coefficient Constraint Tool Calculate polynomial double root coefficient constraint from explicit caller-supplied inputs.
- Polynomial Evaluator Evaluate a polynomial at a point using Horner's method with highest-degree-first coefficients.
- Polynomial Even Odd Part Coefficient Tool One scalar coefficient of the parity decomposition, indexed by its supplied exponent.
- Polynomial Missing Degree Padding Tool Pad a sparse polynomial into ascending degree order through an explicit maximum degree. Duplicate or out-of-range degrees are rejected.
- Polynomial Root Reciprocal Map Map an explicit nonzero real root to its reciprocal for polynomial coefficient reversal, without solving a polynomial.
- Polynomial Root Zero Multiplicity From Prefix Tool Compute polynomial root zero multiplicity from prefix from explicit bounded inputs.
- Polynomial Single Coefficient Unit Rescale Rescale one explicit ascending-power polynomial coefficient for substitution x=argumentScale*y, with degree-zero scale interpreted as one.
- Polynomial Zero Coefficient Run Tool Count a literal zero run in explicitly ordered polynomial coefficients without tolerance-based trimming.
- Quadratic Completing Square Offset Tool Calculate quadratic completing square offset from explicit caller-supplied inputs.
- Quadratic Discriminant Roundoff Scale Tool Compute quadratic discriminant roundoff scale from explicit bounded inputs.
- Quadratic Equation Solver Solve a*x^2 + b*x + c = 0 with explicit discriminant branches; degenerate a = 0 equations fall back to honest linear, no-solution or all-real-numbers cases.
- Quadratic Root Separation From Discriminant Tool Compute quadratic root separation from discriminant from explicit bounded inputs.
- Quadratic Root Sum Scale Residual Tool Compare a supplied scaled quadratic root sum to Vieta’s coefficient ratio without solving for roots.
- Quadratic Vertex Coordinate Unit Change Tool Affine coordinate-unit transformation of a supplied quadratic vertex.
- Quartic Root Product From Coefficients Tool Calculate quartic root product from coefficients from explicit caller-supplied inputs.
- Rational Expression Hole Substitution Tool Evaluate an explicitly supplied reduced rational polynomial in ascending coefficient order, separately flagging a caller-identified excluded point of the original expression. At that point the value is the continuous extension, not the undefined original expression.
- Rational Function Infinity Order Tool Calculate rational function infinity order from explicit caller-supplied inputs.
- Rational Function Pole Order From Orders Tool Compute rational function pole order from orders from explicit bounded inputs.
- Rational Function Zero Order From Orders Tool Compute rational function zero order from orders from explicit bounded inputs.
- Rational Leading Term Sign Tool Determine the rational leading-term sign on a chosen infinite ray from supplied nonzero leading coefficients and degrees.
- Rational Pole Removal Limit Coefficient Tool Local leading-order quotient at a shared zero; zero is a placeholder when a finite limit is unavailable.
- Rational Root Denominator Divisibility Tool Calculate rational root denominator divisibility from explicit caller-supplied inputs.
- Reciprocal Polynomial Coefficient Index Tool Calculate reciprocal polynomial coefficient index from explicit caller-supplied inputs.
- Resultant Linear Linear Term Tool Calculate resultant linear linear term from explicit caller-supplied inputs.
- Symmetric Root Pair Square Sum Tool Calculate symmetric root pair square sum from explicit caller-supplied inputs.
- Synthetic Division Calculator Divide a polynomial (highest-degree-first coefficients) by (x - r) using synthetic division, returning the quotient and remainder.
- Vieta Root Product Residual Tool Compare a supplied pair of roots with the quadratic Vieta product c/a.