Polynomial Tools

Browse all available polynomial tools.

Available tools

Polynomial Antiderivative Coefficient List Integrate ascending-power polynomial coefficients with an explicitly supplied integration constant; bounded number arithmetic, no symbolic rational simplification.
Polynomial Coefficient Convolution Product Multiply two ascending-power polynomial coefficient lists by convolution and normalize high-power exact zeros; no FFT or symbolic integer arithmetic.
Polynomial Coefficient Degree Profile Profile true versus stored degree of ascending-power coefficients; zero polynomial degree is explicitly null instead of silently zero.
Polynomial Coefficient Leading Zero Normalizer Normalize leading-power zeros in ascending-power polynomial coefficients, preserving the zero polynomial as [0]; no approximate-zero pruning.
Polynomial Coefficient Power Padding Pad high powers of an ascending coefficient list to at least an explicit degree without truncating existing high powers; bounded vector output.
Polynomial Coefficient Power Selector Select one ascending polynomial power coefficient, distinguishing implicit zero beyond stored degree from an explicit supplied zero.
Polynomial Coefficient Sign Variation Count Count polynomial coefficient sign variations ignoring exact zeros in ascending order; this is algebraic evidence, not an exact positive-root count.
Polynomial Dense from Power Pairs Build bounded dense ascending coefficients by summing explicit sparse power occurrences into a supplied maximum degree; duplicates are summed, missing powers are zeros.
Polynomial Derivative Coefficient List Differentiate a nonempty ascending-power polynomial coefficient vector exactly under finite number arithmetic; constant polynomial derivative is [0].
Polynomial Even Odd Power Partition Partition p(x) into same-width even-power and odd-power coefficient vectors, with p=even+odd under ascending-power convention.
Polynomial Input Negation Transform Transform ascending coefficients from p(x) to p(-x), flipping odd powers only and preserving stored zeros.
Polynomial Input Scale Transform Transform ascending coefficients from p(x) to p(scale*x); differs from output scaling and retains explicit high-power zero coefficients.
Polynomial Input Translation Transform Translate polynomial input to p(x+offset) by bounded binomial expansion of ascending coefficients; does not approximate or fit coefficients.
Polynomial Low Power Remainder Split ascending polynomial coefficients into remainder modulo x^k and quotient by x^k; not general polynomial long division.
Polynomial Power Shift Transform Multiply an ascending coefficient polynomial by x^shift using exact zero padding; nonnegative shifts only, bounded stored vector size.
Polynomial Sparse Power Pair Extractor Extract nonzero ascending polynomial power/coefficient records; explicit zero powers are intentionally omitted and exact equality is used.
Polynomial Truncated Coefficient Product Return polynomial product coefficients only through an explicit maximum power, equivalent to reduction modulo x^(degree+1); no coefficient rounding.
Polynomial Value Slope Pair Evaluate a nonempty ascending-power polynomial and derivative at one finite x using Horner arithmetic; no root or stability claim.