The coefficient matrix of AX + XB = C against the answer, to n = 100

At its defaults it draws the coefficient matrix of ax + xb = c against the answer, to n = 100. At n = 100 the unknown X has 10000 entries and the coefficient matrix of the linear map has 10⁸ — 0.80 gigabytes of doubles. Eliminating it costs 6.67·10¹¹ operations against the 6·10⁷ Bartels and Stewart's algorithm needs, a ratio of 11111. The Kronecker form is what the equation means and it is not a method.

kronecker-size is one function in lib/figures/sylvester.js — matrix equations — the n²×n² coefficient matrix nobody forms, and sep. Everything below came out of it during this build, at arguments taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

At n = 100 the unknown X has 10000 entries and the coefficient matrix of the linear map has 10⁸ — 0.80 gigabytes of doubles. Eliminating it costs 6.67·10¹¹ operations against the 6·10⁷ Bartels and Stewart's algorithm needs, a ratio of 11111. The Kronecker form is what the equation means and it is not a method.

At n = 100 the unknown X has 10000 entries and the coefficient matrix of the linear map has 10⁸ — 0.80 gigabytes of doubles. Eliminating it costs 6.67·10¹¹ operations against the 6·10⁷ Bartels and Stewart's algorithm needs, a ratio of 11111. The Kronecker form is what the equation means and it is not a method.

At n = 20 the unknown X has 400 entries and the coefficient matrix of the linear map has 1.6·10⁵ — 0.00 gigabytes of doubles. Eliminating it costs 4.27·10⁷ operations against the 4.8·10⁵ Bartels and Stewart's algorithm needs, a ratio of 89. The Kronecker form is what the equation means and it is not a method.

At n = 50 the unknown X has 2500 entries and the coefficient matrix of the linear map has 6.25·10⁶ — 0.05 gigabytes of doubles. Eliminating it costs 1.04·10¹⁰ operations against the 7.5·10⁶ Bartels and Stewart's algorithm needs, a ratio of 1389. The Kronecker form is what the equation means and it is not a method.

At n = 200 the unknown X has 40000 entries and the coefficient matrix of the linear map has 1.6·10⁹ — 12.80 gigabytes of doubles. Eliminating it costs 4.27·10¹³ operations against the 4.8·10⁸ Bartels and Stewart's algorithm needs, a ratio of 88889. The Kronecker form is what the equation means and it is not a method.

At n = 400 the unknown X has 160000 entries and the coefficient matrix of the linear map has 2.56·10¹⁰ — 204.80 gigabytes of doubles. Eliminating it costs 2.73·10¹⁵ operations against the 3.84·10⁹ Bartels and Stewart's algorithm needs, a ratio of 711111. The Kronecker form is what the equation means and it is not a method.

Every figure above checked its own claims on the way to being drawn, and a claim that failed would have stopped the picture rather than shipped a wrong one. Those checks used to leave no trace at all: a passing one returned true and the only evidence the figure had checked anything was that nothing crashed. The list below is what they actually said, collected by running this generator with an observer installed — not a description of what it is believed to check.

3 distinct claims across 6 sets of arguments, grouped below by shape — because most of them are one sentence with a different number in it, and how many separate times that sentence was put to the test is the informative part.

The rule does not apply to it. It factorises nothing, so there is no residual it could be withholding. That is worth stating rather than leaving blank: a site that reported the rule as satisfied by every generator would be counting mostly generators the rule never reached.

Across the library: the rule bites on 217 of 397 generators — 199 print a residual and 18 are exempt with a published reason; 180 factorise nothing. Read from lib/residual-rule.js, which is the same body the gate enforces from, and the gate's last check fails the build if this page and it disagree about any generator.