SbNRN on Sulprobil

Linear Equations with Rational Coefficients (VBA)

Wed, 20 May 2026 04:32:00 +0100

Abstract

Linear equations of the form A * x = b with the non-singular quadratic matrix A and the result vector b have a unique solution because the determinant of A is not zero. If the coefficients of A and of b are rational numbers then the solution is also rational.

Literature

(External Link!) Oliver Aberth, A method for exact computation with rational numbers, JCAM, vol 4, no. 4, 1978

Quota Change as Fraction (Excel/VBA)

Wed, 20 May 2026 04:27:00 +0100

Abstract

Sometimes you need to present quota changes in a simple way. You can achieve this with fractions:

Example: Miller, Smith, and Schulz form a joint heirship. Smith dies without an heir. His quota will be distributed. Schulz also dies. His widows will receive 2/3 of his quota, his only child will get 1/3. Please note that you need to enter this as =1/3 * 2/3 resp. =1/3 * 1/3 whereby the first 1/3 represents Schulz’ original quota.

sbNRN (VBA)

Wed, 20 May 2026 04:25:00 +0100

“God made the integers, all the rest is the work of man.” [Leopold Kronecker]

Abstract

Which rational number is a good proxy of π (3.1415926…)? Enter in cell A1 ‘=pi()’, in cell B1 your maximal denominator (for example 10), and in cells C1:D1 ‘=sbNRN(A1,B1)' as array formula (with CTRL + SHIFT + ENTER). You will get in C1:D1 22 and 7. That means: 22/7 is the nearest rational number to π with a denominator not higher than 10. For 1000 in B1 you would get 355/113.

SbNRN on Sulprobil

Linear Equations with Rational Coefficients (VBA)

Abstract

See also

Literature

Quota Change as Fraction (Excel/VBA)

Abstract

sbNRN (VBA)

Abstract