Symbolic variables

Simple Variable Creation

Create a symbolic variable with @giac_var:

using Giac

@giac_var a
@giac_var a

a + b

# or simply

@giac_var a b

Batch Variable Creation

Create multiple indexed symbolic variables with @giac_several_vars:

using Giac

# 1D vector of variables
@giac_several_vars a 3
# Creates: a1, a2, a3
# Returns: (a1, a2, a3)
a1 + a2 + a3  # Symbolic sum

# 2D matrix of variables
@giac_several_vars m 2 3
# Creates: m11, m12, m13, m21, m22, m23 (row-major order)
# Returns: (m11, m12, m13, m21, m22, m23)

# N-dimensional tensors
@giac_several_vars t 2 2 2
# Creates: t111, t112, t121, t122, t211, t212, t221, t222

# Large dimensions use underscore separators
@giac_several_vars b 2 10
# Creates: b_1_1, b_1_2, ..., b_2_10

# Unicode base names supported
@giac_several_vars α 2
# Creates: α1, α2

# Capture return tuple for iteration
vars = @giac_several_vars c 4
for v in vars
    println(v)
end

Symbolic Comparisons and Inequalities

The comparison operators <, >, <=, >= return symbolic inequality expressions (GiacExpr), not booleans. This enables natural syntax for building constraints:

using Giac

@giac_var x y

# Build symbolic inequalities
x > 0        # Returns a GiacExpr representing x>0
x < y        # Returns a GiacExpr representing x<y
x >= 1//2    # Works with Rational
x <= π       # Works with Irrational

Combine inequalities with & (and) and | (or):

(x > 0) & (x < 10)    # GIAC "and" expression
(x < -1) | (x > 1)    # GIAC "or" expression

Assumptions on Variables

Use assume and additionally to declare constraints on symbolic variables. Subsequent computations will respect these assumptions:

using Giac
using Giac.Commands: assume, about, sign, purge, additionally, sqrt

@giac_var x

# Declare x as positive
assume(x > 0)
sign(x)      # Returns 1
sqrt(x^2)    # Returns x (simplified thanks to assumption)

# Interval constraint using &
assume((x > 0) & (x < 10))
about(x)     # Shows interval [0, 10]

# Or use assume + additionally
assume(x > -1)
additionally(x < 1)
about(x)     # Shows interval [-1, 1]

# Clear assumptions
purge(x)

assume(x > 0)
additionally(x < 10)
# x > 0 now evaluates to "true" (GIAC knows x is positive)
assume(x > 0)  # ERROR: assume(true) is invalid

# Fix: always purge before re-assuming
purge(x)
assume(x > 0)  # Works