Although XCAS is an open source free software, it is still very strong in some aspects, such as dealing with the trigonometric simplification problem.
Less nonsense, please see the XCAS code
Code:
simplify(product(sin(k*pi/214),k,1,106))
XCAS got the exact answer
Code:
(sqrt(107))/81129638414606681695789005144064
We are looking at the performance of Maple2018
Code:
simplify(product(sin(k*pi/214),k=1..106),trig)
But given a bloated answer
Code:
/101 \ /51 \ /103 \ /52 \ /105 \ /
sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|
\214 / \107 / \214 / \107 / \214 / \
53 \ /67 \ /34 \ /69 \ /35 \ /71
--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi
107 / \214 / \107 / \214 / \107 / \214
\ /36 \ /73 \ /37 \ /75 \ /38 \
| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi|
/ \107 / \214 / \107 / \214 / \107 /
/77 \ /39 \ /79 \ /40 \ /81 \ /
sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|
\214 / \107 / \214 / \107 / \214 / \
41 \ /83 \ /42 \ /85 \ /43 \ /87
--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi
107 / \214 / \107 / \214 / \107 / \214
\ /44 \ /89 \ /45 \ /91 \ /46 \
| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi|
/ \107 / \214 / \107 / \214 / \107 /
/93 \ /47 \ /95 \ /48 \ /97 \ /
sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|
\214 / \107 / \214 / \107 / \214 / \
49 \ /99 \ /50 \ /33 \ /17 \ /35
--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi
107 / \214 / \107 / \214 / \107 / \214
\ /18 \ /37 \ /19 \ /39 \ /20 \
| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi|
/ \107 / \214 / \107 / \214 / \107 /
/41 \ /21 \ /43 \ /22 \ /45 \ /
sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|
\214 / \107 / \214 / \107 / \214 / \
23 \ /47 \ /24 \ /49 \ /25 \ /51
--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi
107 / \214 / \107 / \214 / \107 / \214
\ /26 \ /53 \ /27 \ /55 \ /28 \
| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi|
/ \107 / \214 / \107 / \214 / \107 /
/57 \ /29 \ /59 \ /30 \ /61 \ /
sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|
\214 / \107 / \214 / \107 / \214 / \
31 \ /63 \ /32 \ /65 \ /33 \ / 1
--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi
107 / \214 / \107 / \214 / \107 / \214
\ / 1 \ / 3 \ / 2 \ / 5 \ / 3 \
| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi|
/ \107 / \214 / \107 / \214 / \107 /
/ 7 \ / 4 \ / 9 \ / 5 \ /11 \ /
sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|
\214 / \107 / \214 / \107 / \214 / \
6 \ /13 \ / 7 \ /15 \ / 8 \ /17
--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi
107 / \214 / \107 / \214 / \107 / \214
\ / 9 \ /19 \ /10 \ /21 \ /11 \
| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi|
/ \107 / \214 / \107 / \214 / \107 /
/23 \ /12 \ /25 \ /13 \ /27 \ /
sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|
\214 / \107 / \214 / \107 / \214 / \
14 \ /29 \ /15 \ /31 \ /16 \
--- pi| sin|--- pi| sin|--- pi| sin|--- pi| sin|--- pi|
107 / \214 / \107 / \214 / \107 /
Let's take a look at the performance of Wolfram Mathematica 11.3
Code:
FullSimplify@Product[Sin[k*Pi/214], {k, 1, 106}]
For a long time, it is estimated that it has not been calculated.
But still give the answer, but it is very bad
Code:
(Csc[\[Pi]/214]^3 Csc[(3 \[Pi])/214] Csc[(5 \[Pi])/214]^2 Csc[(
7 \[Pi])/214] Csc[(9 \[Pi])/214]^4 Csc[(11 \[Pi])/214] Csc[(
13 \[Pi])/214]^2 Csc[(15 \[Pi])/214] Csc[(17 \[Pi])/214]^3 Csc[(
19 \[Pi])/214] Csc[(21 \[Pi])/214]^2 Csc[(23 \[Pi])/214] Csc[(
25 \[Pi])/214]^5 Csc[(27 \[Pi])/214] Csc[(29 \[Pi])/214]^2 Csc[(
31 \[Pi])/214] Csc[(33 \[Pi])/214]^3 Csc[(35 \[Pi])/214] Csc[(
37 \[Pi])/214]^2 Csc[(39 \[Pi])/214] Csc[(41 \[Pi])/214]^4 Csc[(
43 \[Pi])/214] Csc[(45 \[Pi])/214]^2 Csc[(47 \[Pi])/214] Csc[(
49 \[Pi])/214]^3 Csc[(51 \[Pi])/214] Csc[(53 \[Pi])/
214]^2 Sin[\[Pi]/107]^4 Sin[(2 \[Pi])/107] Sin[(3 \[Pi])/
107]^2 Sin[(4 \[Pi])/107] Sin[(5 \[Pi])/107]^3 Sin[(6 \[Pi])/
107] Sin[(7 \[Pi])/107]^2 Sin[(8 \[Pi])/107] Sin[(9 \[Pi])/
107]^5 Sin[(10 \[Pi])/107] Sin[(11 \[Pi])/107]^2 Sin[(12 \[Pi])/
107] Sin[(13 \[Pi])/107]^3 Sin[(14 \[Pi])/107] Sin[(15 \[Pi])/
107]^2 Sin[(16 \[Pi])/107] Sin[(17 \[Pi])/107]^4 Sin[(18 \[Pi])/
107] Sin[(19 \[Pi])/107]^2 Sin[(20 \[Pi])/107] Sin[(21 \[Pi])/
107]^3 Sin[(22 \[Pi])/107] Sin[(23 \[Pi])/107]^2 Sin[(24 \[Pi])/
107] Sin[(25 \[Pi])/107]^6 Sin[(26 \[Pi])/
107])/40564819207303340847894502572032
So, XCAS wins
Since the HP prime RAM memory is too small, it is restarted.
Looking forward to hp prime's first new firmware update in 2019, expecting CAS update to 1.51-29
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