Cross term
A cross term is a product involving two distinct variables, functions, or other terms that represents their interaction.
Elliptic Curve Cryptography for Developers
A cross term is a product involving distinct Lagrange interpolant functions that arises when sums of those functions are multiplied.
- How it is used
- Collects mixed Lagrange products into the h(x)t(x) component needed to construct QAP-based proof data.
- How deep it goes
- Derives a general factorization, counts and tabulates coefficients, and maps the result to C routines for precomputation and proof creation.
- Examples
- Works through l_0(x)l_1(x), a five-gate QAP with ten pairs, coefficient tables, and C routines that compute and aggregate them.
- What you can do after
- Build it from scratch by enumerating interpolant pairs, expanding coefficients, weighting rows, and aggregating the h(x) coefficient vector.
Read how Elliptic Curve Cryptography for Developers explains cross term →
Experimentation for Engineers
A regression term formed by multiplying two distinct predictor variables to represent their joint effect.
- How it is used
- Models joint effects between two continuous parameters during response-surface interpolation and optimization.
- How deep it goes
- Defines the term, explains diagonal interpolation, and demonstrates fitting and grid evaluation, while stopping at two practical parameters.
- Examples
- Uses threshold and order_size, the x0x1 design-matrix column, and a central-composite experiment with measured and interpolated responses.
- What you can do after
- Build it from scratch by adding the pairwise product to a NumPy regression matrix and evaluating the resulting surrogate surface.
Read how Experimentation for Engineers explains cross term →
Related concepts
- quadratic modelused by · A response model containing constant, linear, squared, and possibly pairwise-product terms of its predictors.
- lagrange polynomialuses · A Lagrange polynomial is a polynomial associated with Lagrange interpolation, including basis polynomials and their data-weighted interpolating sum.
- interpolationproduced by · Interpolation is the estimation or construction of values or representations between known points according to an assumed relationship or specified rule.
- quadratic arithmetic programpart of · A quadratic arithmetic program is a polynomial constraint representation of an arithmetic computation in which the computation's validity is expressed through quadratic polynomial relationships.
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