a few Maple10/11 projects Wave Deconstruct / reconstruct Is/If with Assuming in Maple A Maple coffee table Calculate area between two curves HTML color codes using Maple
about this document get Maple 11 ! is_if_DOC.mw  ( Maple 11 worksheet archive ) updated 4-9-07 

is(...) or if with assuming...to each it's own 

if assuming...      returns true if any condition satisfies the test
is(...) assuming... returns true if all conditions satisfy the test 

======================================================

Typesetting:-mrow(Typesetting:-mi(
Typesetting:-mrow(Typesetting:-mi(
`+`(`/`(2, 3), `-`(`*`(2, `*`(n))))

Typesetting:-mrow(Typesetting:-mi(

Typesetting:-mrow(Typesetting:-mi(
Typesetting:-mrow(Typesetting:-mi(
Plot_2d

Typesetting:-mrow(Typesetting:-mi(
Typesetting:-mrow(Typesetting:-mi(
Typesetting:-mrow(Typesetting:-mi(
Plot_2d

Typesetting:-mrow(Typesetting:-mi(
-.5133333333

Typesetting:-mrow(Typesetting:-mi(

.2666666667

# using if the return is true if any condition satisfies the test
Typesetting:-mrow(Typesetting:-mo(
Typesetting:-mrow(Typesetting:-mo(
true

Typesetting:-mrow(Typesetting:-mo(
Typesetting:-mrow(Typesetting:-mo(
true

Typesetting:-mrow(Typesetting:-mo(
Typesetting:-mrow(Typesetting:-mo(
true

Typesetting:-mrow(Typesetting:-mo(
false

Typesetting:-mrow(Typesetting:-mo(
true


# using  is the return is true if all conditions satisfies the test
Typesetting:-mrow(Typesetting:-mo(
Typesetting:-mrow(Typesetting:-mi(
false

Typesetting:-mrow(Typesetting:-mo(
Typesetting:-mrow(Typesetting:-mi(
true

Typesetting:-mrow(Typesetting:-mo(
Typesetting:-mrow(Typesetting:-mi(
false

Typesetting:-mrow(Typesetting:-mi(
false

Typesetting:-mrow(Typesetting:-mi(
true

# redefine intx to use as a function, find the place between -.1 and -1 where/if total area is near zero  ( .0001 resolution )
`:=`(intx, proc (n) options operator, arrow; int(`+`(`*`(`^`(x, 2)), `-`(n)), x = -1 .. 1) end proc); 1
proc (n) options operator, arrow; int(`+`(`*`(`^`(x, 2)), `-`(n)), x = -1 .. 1) end proc

`:=`(bFound, false); -1; `:=`(n, .1); -1; for k to 1000 do `:=`(n, `+`(n, 0.1e-1)); if `<>`(`+`(intx(n), `-`(abs(intx(n)))), 0) then `:=`(bFound, true); break end if end do; -1; if bFound = true then ...
`:=`(bFound, false); -1; `:=`(n, .1); -1; for k to 1000 do `:=`(n, `+`(n, 0.1e-1)); if `<>`(`+`(intx(n), `-`(abs(intx(n)))), 0) then `:=`(bFound, true); break end if end do; -1; if bFound = true then ...
`:=`(bFound, false); -1; `:=`(n, .1); -1; for k to 1000 do `:=`(n, `+`(n, 0.1e-1)); if `<>`(`+`(intx(n), `-`(abs(intx(n)))), 0) then `:=`(bFound, true); break end if end do; -1; if bFound = true then ...
`:=`(bFound, false); -1; `:=`(n, .1); -1; for k to 1000 do `:=`(n, `+`(n, 0.1e-1)); if `<>`(`+`(intx(n), `-`(abs(intx(n)))), 0) then `:=`(bFound, true); break end if end do; -1; if bFound = true then ...
.34






 

Plot_2d
total area = 0 +- .0001
( each section is near equal )

# integrate the final result
Plot_2d
Plot_2d


Get Maple 11 !
Tim Van Dusen  4-8-07

































































 

  what is this?

  The worksheet began as an attempt to analyze the difference in which Maple's  assumming  is handled by the Maple  is(...)  function in comparison with the way it is handled with the   if  conditional.

A short while into the worksheet I became curious as to whether some of what I was doing within the worksheet could also be used to move the  x^2  plot along the y axis in such a way to produce an area near zero within the -1..1 range along the x-axis. I demonstrate the process within the lower half of the worksheet. It appears as though a definitive area of zero cannot be obtained without adjusting the span of the x axis as well.

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