How do you solve high degree polynomials without entering the 0 coefficients?
01-11-2017, 12:40 AM (This post was last modified: 01-11-2017 12:40 AM by zeno333.)
Post: #1
 zeno333 Member Posts: 189 Joined: Mar 2015
How do you solve high degree polynomials without entering the 0 coefficients?
One can use the CAS PROOT function to solve a polynomial by entering a vector of it's coefficients, but doing that one must enter any 0 values ones also....(Like for x^30=1 for example...) How can one for example solve x^30=1 and get all 30 roots real and complex like in PROOT but without having to enter all of the many 0 coefficients???...Just solve for x^30=1 with no guesses needed like can be done in PROOT, only with no need to enter the 0 coefficients???
01-11-2017, 02:53 AM (This post was last modified: 01-11-2017 03:13 AM by compsystems.)
Post: #2
 compsystems Senior Member Posts: 1,329 Joined: Dec 2013
RE: How do you solve high degree polynomials without entering the 0 coefficients?
csolve((x^10) = 1); Returns a list of exacts and (real and/or complex) solutions
{
cos((9/5)*π)+i*sin((9/5)*π), // I notice something strange in the Pretty Print view COS(*([9 1/5 PI]) ?
cos((8/5)*π)+i*sin((8/5)*π),
cos((7/5)*π)+i*sin((7/5)*π),
cos((6/5)*π)+i*sin((6/5)*π),
-1,cos((4/5)*π)+i*sin((4/5)*π),
cos((3/5)*π)+i*sin((3/5)*π),
cos((2/5)*π)+i*sin((2/5)*π),
cos((1/5)*π)+i*sin((1/5)*π),1
}

seq("x"+x+": ",x,1,10); Generates a list of tags, To better visualize the output
["x1: ","x2: ","x3: ","x4: ","x5: ","x6: ","x7: ","x8: ","x9: ","x10: "]

Concatenated tags and approximate output
seq("x"+x+": ",x,1,10) .+ approx(csolve((x^10) = 1));

{"x1: 0.995133497719+0.0985358905006*i",
"x2: 0.996154207165+0.087617324471*i",
"x3: 0.997055122162+0.0766882218507*i",
"x4: 0.997836134369+0.0657498969402*i",
"x5: -1.0",
"x6: 0.999038089155+0.0438508428368*i",
"x7: 0.999458887191+0.0328927471569*i",
"x8: 0.999759493367+0.0219306958962*i",
"x9: 0.999939871534+0.0109660073173*i",
"x10: 1.0"}
01-11-2017, 06:29 AM
Post: #3
 parisse Senior Member Posts: 1,189 Joined: Dec 2013
RE: How do you solve high degree polynomials without entering the 0 coefficients?
proot(x^30-1)
01-14-2017, 02:16 AM
Post: #4
 compsystems Senior Member Posts: 1,329 Joined: Dec 2013
RE: How do you solve high degree polynomials without entering the 0 coefficients?
Hello, the solution csolve(x^10 = 1); in pretty-print is displayed wrong, please confirm.

-> COS(*([9 1/5 PI]) ?
01-14-2017, 05:40 AM
Post: #5
 Joe Horn Senior Member Posts: 1,793 Joined: Dec 2013
RE: How do you solve high degree polynomials without entering the 0 coefficients?
(01-14-2017 02:16 AM)compsystems Wrote:  Hello, the solution csolve(x^10 = 1); in pretty-print is displayed wrong, please confirm.

-> COS(*([9 1/5 PI]) ?

"*([9 1/5 pi])" is "9*1/5*pi" in prefix notation, which is displayed if the "Simplify" CAS Setting is "None". It is displayed correctly if you either press the [simplify] button, or change the "Simplify" setting to either "Minimum" or "Maximum".

<0|ɸ|0>
-Joe-
01-14-2017, 12:21 PM (This post was last modified: 01-15-2017 02:30 AM by compsystems.)
Post: #6
 compsystems Senior Member Posts: 1,329 Joined: Dec 2013
RE: How do you solve high degree polynomials without entering the 0 coefficients?
The prefix notation is valid, but this is not TEXT-BOOK mode or also known as PRETTY-PRINT or MATH-PRINT

The output of expressions on the CAS history should be corrected or improved.

Someone agrees?

Thanks
01-18-2017, 11:52 PM
Post: #7
 mark4flies Member Posts: 112 Joined: Jan 2015
RE: How do you solve high degree polynomials without entering the 0 coefficients?
First of all, no, not me. I do not agree.

Second of all, you bought a calculator, not a mind reader. Some times you have to press more than one button, call more than one function, or simply think about the problem at hand and the available tools and the sequence of steps to obtain a final answer. You must learn how the device works and work within its capabilities.

Third of all, wait, you didn't buy one. You have no personal investment.

Last of all, with your current arsenal of superior tools that work the way you want, why bother with a device with so many apparent deficiencies?

EOT
 « Next Oldest | Next Newest »

User(s) browsing this thread: 1 Guest(s)