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Beta HP Prime 13011/13012: résultats exacts

Re: Beta HP Prime 13011/13012: résultats exacts

Unread postby critor » 19 Nov 2017, 10:51

We already have similar programs trying to "guess" an exact value from a decimal result, which are even supporting the
$mathjax$\frac{\pm a\sqrt{b} \pm c\sqrt{d}}{f}$mathjax$
form missing for the HP Prime.
No wonder, since the official
toExact()
feature on TI-z80 and -Nspire calculators is only looking for a matching
$mathjax$\frac{a}{b}$mathjax$
form.
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Re: Beta HP Prime 13011/13012: résultats exacts

Unread postby compsystems » 19 Nov 2017, 16:28

Ok, but the problem of the ti68K and tinspire do not have a flag to override the automatic simplification, for this reason the expression must be shown between strings, not in prettyprint.

It is very useful that in future versions the developers of the tinspire, add a flag to eliminate the automatic simplification as does the hp-prime

Examples


Code: Select all
ex#0:
qpirlne( (2*π/3)+(3*π/4) , 0)  -> 17/12*π

qpirlne( (2*π/3)+(3*π/4) , 1)  -> 1137949/255685 // Q1

qpirlne( (2*π/3)+(3*π/4) , 2)  -> 4+(115209/255685) // Q2

qpirlne( (2*π/3)+(3*π/4) , 3)  ->  17/12*π // PI

qpirlne( (2*π/3)+(3*π/4) , 4)  ->  (2*π/3)+(3*π/4) // ROOT

qpirlne( (2*π/3)+(3*π/4) , 5)  ->  (2*π/3)+(3*π/4) // LN

qpirlne( (2*π/3)+(3*π/4) , 6)  ->  (2*π/3)+(3*π/4) // e

ex#1:
qpirlne( LN(3*π)-LN(√(5)), 0)  -> LN( (3*π*√(5)/5) )
qpirlne( LN(3*π)-LN(√(5)), 1)  -> 55715/38728 // Q1
qpirlne( LN(3*π)-LN(√(5)), 2)  -> 1+(16987/38728) // Q2
qpirlne( LN(3*π)-LN(√(5)), 3)  -> LN( (3*π*√(5)/5) )  // PI
qpirlne( LN(3*π)-LN(√(5)), 4)  -> LN( (3*π*√(5)/5) )  // ROOT
qpirlne( LN(3*π)-LN(√(5)), 5)  -> LN( (3*π*√(5)/5) ) // LN
qpirlne( LN(3*π)-LN(√(5)), 6)  -> LN(3*π)-LN(√(5)) // e

ex#2:
qpirlne( LN((2/5))-LN(√(2)), 0)  -> -LN((25/2))/2
qpirlne( LN((2/5))-LN(√(2)), 1)  -> -116599/92329 // Q1
qpirlne( LN((2/5))-LN(√(2)), 2)  -> -1+(-24270/92329) // Q2
qpirlne( LN((2/5))-LN(√(2)), 3)  -> LN((2/5))-LN(√(2)) // PI
qpirlne( LN((2/5))-LN(√(2)), 4)  -> LN((2/5))-LN(√(2)) // ROOT
qpirlne( LN((2/5))-LN(√(2)), 5) -> -LN((25/2))/2 // LN
qpirlne( LN((2/5))-LN(√(2)), 6)  -> LN((2/5))-LN(√(2)) // e

ex#3:

qpirlne( e^(2*π/(3*√(7))), 0)  -> e^((2*π*√(7)/21))
qpirlne( e^(2*π/(3*√(7))), 1)  -> 224192/101585 // Q1
qpirlne( e^(2*π/(3*√(7))), 2)  -> 1+(21022/101585) // Q2
qpirlne( e^(2*π/(3*√(7))), 3)  -> e^(2*π/(3*√(7))) // PI
qpirlne( e^(2*π/(3*√(7))), 4)  -> e^(2*π/(3*√(7))) // ROOT
qpirlne( e^(2*π/(3*√(7))), 5)  -> e^(2*π/(3*√(7))) // LN
qpirlne( e^(2*π/(3*√(7))), 6)  -> e^(2*π/(3*√(7))) // e


ex#4:
qpirlne( 7*π/√(90), 0)  -> 7*π*√(10)/30

qpirlne( 7*π/√(90), 1)  -> 171470/73971

qpirlne( 7*π/√(90), 2)  -> 260521/112387

qpirlne( 7*π/√(90), 3)  -> 7*π/√(90)


ex#5:
qpirlne( 1/(3+i*√(3)), 0)  -> (1/4)-i*((√(3)/12))
qpirlne( 1/(3+i*√(3)), 1)  -> (1/4)-(1/4)*i*√(1/3) // Q1
qpirlne( 1/(3+i*√(3)), 2)  -> (1/4)-(i*37829/262087) // Q1
qpirlne( 1/(3+i*√(3)), 3)  -> 1/(3+i*√(3)) // PI
qpirlne( 1/(3+i*√(3)), 4)  -> (1/4)-i*((√(3)/12)) // ROOT
qpirlne( 1/(3+i*√(3)), 5)  -> 1/(3+i*√(3)) // LN
qpirlne( 1/(3+i*√(3)), 6)  -> 1/(3+i*√(3)) // e

ex#6:
qpirlne( ACOS((-1/2)), 0)  -> 2/3*PI
qpirlne( ACOS((-1/2)), 1)  -> 138894/66317 // Q1
qpirlne( ACOS((-1/2)), 2)  -> 2*(6260/66317) // Q2
qpirlne( ACOS((-1/2)), 3)  -> 2/3*PI // PI
qpirlne( ACOS((-1/2)), 4)  -> ACOS((-1/2) // ROOT
qpirlne( ACOS((-1/2)), 5)  -> ACOS((-1/2) // LN
qpirlne( ACOS((-1/2)), 6)  -> ACOS((-1/2) // e

ex#7:
qpirlne( COS((3*π/4)), 0)  -> -√(-2)/2
qpirlne( COS((3*π/4)), 1)  -> -195025/275807 // Q1
qpirlne( COS((3*π/4)), 2)  -> -195025/275807  // Q2
qpirlne( COS((3*π/4)), 3)  -> COS((3*π/4)) // PI
qpirlne( COS((3*π/4)), 4)  -> -√(1/2) // ROOT
qpirlne( COS((3*π/4)), 5)  -> COS((3*π/4)) // LN
qpirlne( COS((3*π/4)), 6)  -> COS((3*π/4)) // e

ex#8:
qpirlne( COS(π/12), 0)  -> (√(3)+1)*(√(2)/4)
qpirlne( COS(π/12), 1)  -> 129209/133767 // Q1
qpirlne( COS(π/12), 2)  -> 272847/282472  // Q2
qpirlne( COS(π/12), 3)  -> COS((3*π/4)) // PI
qpirlne( COS(π/12), 4)  -> (√(3)+1)*(√(2)/4) // ROOT
qpirlne( COS(π/12), 5)  -> COS(π/12) // LN
qpirlne( COS(π/12), 6)  -> COS(π/12) // e

ex#9:
qpirlne( SIN(π/10), 0)  -> (-1+√((5)))/4
qpirlne( SIN(π/10), 1)  -> 98209/317811 // Q1
qpirlne( SIN(π/10), 2)  -> 98209/317811  // Q2
qpirlne( SIN(π/10), 3)  -> SIN(π/10) // PI
qpirlne( SIN(π/10), 4)  -> (-1+√((5)))/4 // ROOT
qpirlne( SIN(π/10), 5)  -> SIN(π/10) // LN
qpirlne( SIN(π/10), 6)  -> SIN(π/10) // e

ex#10:
qpirlne( SIN(π/8), 0)  -> √(2-√(2))/2
qpirlne( SIN(π/8), 1)  -> 69237/180925 // Q1
qpirlne( SIN(π/8), 2)  -> 69237/180925  // Q2
qpirlne( SIN(π/8), 3)  -> SIN(π/8) // PI
qpirlne( SIN(π/8), 4)  -> √(2-√(2))/2 // ROOT
qpirlne( SIN(π/8), 5)  -> SIN(π/8) // LN
qpirlne( SIN(π/8), 6)  -> SIN(π/8) // e

ex#11:
qpirlne( COS(π/5), 0)  -> (1+(√(5)))/4
qpirlne( COS(π/5), 1)  -> 98209/121393 // Q1
qpirlne( COS(π/5), 2)  -> 317811/392836  // Q2
qpirlne( COS(π/5), 3)  -> COS(π/5) // PI
qpirlne( COS(π/5), 4)  ->  (1+(√(5)))/4 // ROOT
qpirlne( COS(π/5), 5)  -> COS(π/5) // LN
qpirlne( COS(π/5),, 6)  -> COS(π/5) // e
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