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Advaced Calculus [Transit operator]

An important knowledge about the Smath integration operator and the Maple companionship.

u F 11 x 2^+ / :

GID integral => Get It Done Integral Curve

z Int u F u x - x int :

Recast the transit operator for the plot AND enable on-line point value of Integral curve

x Int z Int :

1.23456789 Int 0.9782

8 - Int 0.246154 -

Resolving a GID ambiguity

In Int(z), "z" is a dummy transitional scalar that enables the plot over the canvas, a "resourcing vanishing iterator" that must be redefined in term of the variable of integration "x" for the on-line point evaluation and by same token re-enables the quick plot in its default "x scalar". In Φ(u), "u" is also a transitional iterator that interprets the numerical integration operator int(Φ(u),u,-x,x). It is not coincidence it works this way, simply that it has been properly coded GID !

u Φ 11 x 2^+ / :

z Int u Φ u x - x int :

Tools/Options/Calculation/Integral accuracy 10000 ≡

x Plot u Φ u x - x int maple : 2 x * 1 x 2^+ /

DO NOT recast the transit operator Int(x) ... already defined above.

8 - Int 0.246153846153847 -

8 - Plot 0.246153846153846 -

X 4 :

sanity check

XY X X Int + 20 red 15 mat :

Very slow plot ~ 1min.20

x Int XY 2 1 sys

Very fast plot

x Plot XY x Φ 3 1 sys