Tensor Standard Math Calculator

Literals: numbers 2, vectors v(1,2), covectors cv(3,4), matrices m(1,2;3,4), rank-3 t3(a,b;c,d|e,f;g,h). Operators: + - add/sub, * tensor product, @ contract. Functions: trace det inv transpose norm identity raise lower sym antisym eigenvalues contract. GR: christoffel(g, dg) riemann(g, dg, ddg). Indexed: T[a+, b-], contract(T[a+, b-], v[b+]). Basis: components(T, e). Where: v + w where let v = v(1,2); let w = v(3,4).

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Conversion Rules

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Interpretation

Input

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Tensor-form expression

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Symbolic parse tree

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Output

Result value

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Evaluation Trace

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Core Rules

Scalars are rank-0 tensors.

Addition requires identical tensor type.

Tensor product combines structure without collapsing it.

Contraction is explicit and dimension-aware.

Subtraction desugars to A + (-1) * B.

What 1 + 2 means here

1 is promoted to T[] with value 1.

2 is promoted to T[] with value 2.

T[] + T[] is valid because both are rank-0.

Result 3 is also T[]: scalar arithmetic is a special case of tensor arithmetic.

Layer 2 Operations

trace(M) sums diagonal elements of a square matrix.

det(M) computes the determinant (2x2, 3x3).

inv(M) returns the inverse with swapped variance.

transpose(M) swaps rows/cols and variance.

norm(v) returns the Euclidean norm as a scalar.

identity(n) creates an n×n identity matrix.

lower(v, g) lowers a vector with metric g → covector.

raise(ω, g) raises a covector with metric g → vector.

TLS 0.2 Formal specification for a tensor-native symbolic mathematics language

Output will appear here after running.

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Environment

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