Giac: fix calculus command argument slots

[GliAcopo]

Problem

Applying Giac → Calculus → Differentiate to selected structured mathematics immediately evaluated diff(expression) and gave no place to specify a differentiation variable. This is particularly unhelpful for multivariable expressions. Several neighboring calculus actions similarly constructed calls with fewer argument slots than their documented Giac forms.

Reproduction

1. Enter ln(sqrt(x^2 + z^2) + z) as TeXmacs mathematics.
2. Select it.
3. Choose Giac → Calculus → Differentiate.

Previously, the menu used arity 1, so TeXmacs took the immediate-evaluation path for diff(selection). The expected interaction is an editable diff(selection, …) operation where z can be entered.

Root cause

giac-apply delegates non-session operations to TeXmacs' generic script-apply. Its arity controls both the generated argument slots and whether a selected unary operation is evaluated immediately. The Giac Calculus menu supplied unary or otherwise incomplete arities for several commands.

Implementation

Use the practical documented arity for each Calculus action:

• two arguments for differentiation, integration, gradient, divergence, curl, Hessian, Laplacian, extrema, convexity, Taylor, and series;
• three for limits and implicit differentiation.

Optional higher-order, bounded, directional, or constrained forms remain editable by users without expanding this into a command redesign.

Examples

The differentiation action now supports diff(x^2,x), diff(x*y,x), diff(x*y,y), and diff(ln(sqrt(x^2+z^2)+z),z).

Validation

• Parsed the updated Scheme file with Guile.
• Checked the diff for whitespace errors.
• Verified all updated menu mappings and arities.
• Exercised the selection-to-editable-script flow in TeXmacs 2.1.4 with the patched plugin.
• Evaluated representative forms for every changed command with Giac 1.9.0.
• Confirmed the logarithmic derivative is algebraically equivalent to 1/sqrt(x^2+z^2).