Data and Math

vsymbolic

Expression trees you can differentiate and simplify, symbol by symbol.

Released v1.0.0 · 2026-09-28

Import

use "stdlib/symbolic.ven"

Symbolic algebra: building an expression as a tree of values and operations, differentiating it symbolically, and simplifying it algebraically, built on Venutian's own trigonometry, exponential and logarithm builtins together with maps and shapes. It manipulates an expression as data, rather than only evaluating it to a number.

vsymbolic.ven

x = sym_var("x")
print x.kind

Reference (20 functions)

expr_new
sym_const
sym_var
sym_coerce
sym_add
sym_sub
sym_mul
sym_div
sym_pow
sym_neg
sym_sin
sym_cos
sym_exp
sym_ln
bindings_of
sym_evaluate
sym_differentiate
sym_simplify_once
sym_simplify
sym_to_text

API reference

`expr_new(kind, value, name, left, right, arg, exponent)`

sym_to_text(expr_new("const", 7.0, "", nothing, nothing, nothing, 0.0))

`sym_const(v)`

sym_to_text(sym_const(5.0))

`sym_var(name)`

sym_var("x").kind

`sym_coerce(value)`

Coerces a plain Number into a constant Expr, passing an existing Expr through unchanged.

sym_to_text(sym_coerce(9.0))

`sym_add(a, b)`

sym_to_text(sym_add(sym_var("x"), 3.0))

`sym_sub(a, b)`

sym_to_text(sym_sub(sym_var("x"), 3.0))

`sym_mul(a, b)`

sym_to_text(sym_mul(sym_var("x"), 2.0))

`sym_div(a, b)`

sym_to_text(sym_div(sym_var("x"), 2.0))

`sym_pow(a, n)`

sym_to_text(sym_pow(sym_var("x"), 3.0))

`sym_neg(a)`

sym_to_text(sym_neg(sym_var("x")))

`sym_sin(a)`

sym_to_text(sym_sin(sym_var("x")))

`sym_cos(a)`

sym_to_text(sym_cos(sym_var("x")))

`sym_exp(a)`

sym_to_text(sym_exp(sym_var("x")))

`sym_ln(a)`

sym_to_text(sym_ln(sym_var("x")))

`bindings_of(var_name, v)`

Builds a single-variable bindings Map for sym_evaluate.

map_get(bindings_of("x", 2.5), "x")

`sym_evaluate(expr, bindings)`

sym_evaluate(sym_pow(sym_var("x"), 2.0), bindings_of("x", 4.0))

`sym_differentiate(expr, var_name)`

Symbolically differentiates expr with respect to var_name, returning a new Expr.

sym_to_text(sym_simplify(sym_differentiate(sym_pow(sym_var("x"), 2.0), "x")))

`sym_simplify_once(expr)`

Runs one bottom-up simplification pass over expr, returning a new, possibly-smaller Expr.

sym_to_text(sym_simplify_once(sym_add(sym_const(1.0), sym_const(2.0))))

`sym_simplify(expr)`

sym_to_text(sym_simplify(sym_neg(sym_neg(sym_var("x")))))

`sym_to_text(expr)`

Renders expr as a fully-parenthesized Text expression.

sym_to_text(sym_add(sym_var("x"), 3.0))

API reference

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