MaplePrimes - Questions and Posts tagged with coeff
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en-us2016 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSat, 03 Dec 2016 11:38:47 GMTSat, 03 Dec 2016 11:38:47 GMTThe most recent questions and posts on MaplePrimes tagged with coeffhttp://www.mapleprimes.com/images/mapleprimeswhite.jpgMaplePrimes - Questions and Posts tagged with coeff
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Expanding series
http://www.mapleprimes.com/questions/219609-Expanding-Series?ref=Feed:MaplePrimes:Tagged With coeff
<p>I've developed an algorithm for pulling out the nth coefficient in a power series expansion. It requires the exact wavefuntion and the first n-1 correction terms. Here it is:<img src="/view.aspx?sf=219609_question/Screen_Shot_2016-10-30_at_9.29.48_AM.png">Does anyone know how to extend this to a slightly different differential equation say:</p>
<p>DE := diff(psi(x), x, x)-(gamma*x^6+beta*x^4+alpha*x^2-E)*psi(x) = 0</p>
<p>especially for the special case alpha =0.</p>
<p>Thanks in advance</p>
<p>I've developed an algorithm for pulling out the nth coefficient in a power series expansion. It requires the exact wavefuntion and the first n-1 correction terms. Here it is:<img src="/view.aspx?sf=219609_question/Screen_Shot_2016-10-30_at_9.29.48_AM.png">Does anyone know how to extend this to a slightly different differential equation say:</p>
<p>DE := diff(psi(x), x, x)-(gamma*x^6+beta*x^4+alpha*x^2-E)*psi(x) = 0</p>
<p>especially for the special case alpha =0.</p>
<p>Thanks in advance</p>
219609Sun, 30 Oct 2016 09:34:49 ZchomchomchomchomMultiply each term from a polynom by a coefficient
http://www.mapleprimes.com/questions/219337-Multiply-Each-Term-From-A-Polynom-By?ref=Feed:MaplePrimes:Tagged With coeff
<p>Hi there,</p>
<p>I have a big polynomial expression involving powers of x and y, that comes from expanding a function in powers of x and y in polynomial form (I use series(convert(series(a,x=0,10),polynom),y=0,10) ). I want to multiply each of the terms by the factorial of the power of x and y it has. How can I do this?<br>
I tried using Physics[Coefficient](a,x) but I get the error: it cannot compute the degree of the expression.<br>
I tried using a double for with a double coeff to get each of the coefficients and the maybe be able to multiply them but I get the error "unable to compute coeff".</p>
<p>Is it because as expanding the series I have the term +O(y^11) that it cannot compute it?<br>
<br>
<br>
[Edit]<br>
I managed to substitute the x terms using subs(x^3=3!*x^3,x^5=5!*x^5,a). Obviously this is not very efficient since I need to write the substitution for each term, and since the ploynom is grouped in powers of y, this does not work for y (neither does algusbs).<br>
</p>
<p>[Edit 2]:</p>
<p>an example of it would be:<br>
</p>
<p><img alt="restart; z:=1/2*log((1+y+x)/(1+y-x)): a:=diff(z,x)*h: i:=int(series(convert(series(a,x=0,12),polynom),y=0,12),x);" src="http://www.mapleprimes.com/MapleImage.ashx?f=92b31b2ffcf04e24efeecd9402188a28.gif"><br>
with result <br>
<img alt="i := -(1/6)*x^3-(1/8)*x^5-(11/112)*x^7-(31/384)*x^9-(193/2816)*x^11+(x+(2/3)*x^3+(7/10)*x^5+(41/56)*x^7+(109/144)*x^9+(1093/1408)*x^11)*y" src="http://www.mapleprimes.com/MapleImage.ashx?f=a12f19c2b08a2d1a9db718f0aa132654.gif"></p>
<p>And I want the coefficients for each x and y power to be multiplied by the factorial of those powers.</p>
<p> </p>
<p>Thank you!</p>
<p>Hi there,</p>
<p>I have a big polynomial expression involving powers of x and y, that comes from expanding a function in powers of x and y in polynomial form (I use series(convert(series(a,x=0,10),polynom),y=0,10) ). I want to multiply each of the terms by the factorial of the power of x and y it has. How can I do this?<br>
I tried using Physics[Coefficient](a,x) but I get the error: it cannot compute the degree of the expression.<br>
I tried using a double for with a double coeff to get each of the coefficients and the maybe be able to multiply them but I get the error "unable to compute coeff".</p>
<p>Is it because as expanding the series I have the term +O(y^11) that it cannot compute it?<br>
<br>
<br>
[Edit]<br>
I managed to substitute the x terms using subs(x^3=3!*x^3,x^5=5!*x^5,a). Obviously this is not very efficient since I need to write the substitution for each term, and since the ploynom is grouped in powers of y, this does not work for y (neither does algusbs).<br>
</p>
<p>[Edit 2]:</p>
<p>an example of it would be:<br>
</p>
<p><img alt="restart; z:=1/2*log((1+y+x)/(1+y-x)): a:=diff(z,x)*h: i:=int(series(convert(series(a,x=0,12),polynom),y=0,12),x);" src="http://www.mapleprimes.com/MapleImage.ashx?f=92b31b2ffcf04e24efeecd9402188a28.gif"><br>
with result <br>
<img alt="i := -(1/6)*x^3-(1/8)*x^5-(11/112)*x^7-(31/384)*x^9-(193/2816)*x^11+(x+(2/3)*x^3+(7/10)*x^5+(41/56)*x^7+(109/144)*x^9+(1093/1408)*x^11)*y" src="http://www.mapleprimes.com/MapleImage.ashx?f=a12f19c2b08a2d1a9db718f0aa132654.gif"></p>
<p>And I want the coefficients for each x and y power to be multiplied by the factorial of those powers.</p>
<p> </p>
<p>Thank you!</p>
219337Tue, 18 Oct 2016 12:00:32 ZOsBOsBAssume products of variables are zero in large set of polynomial equations
http://www.mapleprimes.com/questions/218613-Assume-Products-Of-Variables-Are-Zero?ref=Feed:MaplePrimes:Tagged With coeff
<p>I am interested in the behaviour of a system of equations close to the origin- these equations are quite long, and there are a lot of them so i would like to have commands that i can use to assume products of variables are zero. </p>
<p>here are the first two polynomials:</p>
<p><br>alpha*k[a1]*B[1]^2+(-alpha*k[a1]-alpha*k[a2])*B[2]*B[1]+2*alpha*k[a1]*B[1]*B[11]+alpha*k[a1]*B[12]*B[1]+2*alpha*k[a1]*B[1]*B[211]+alpha*k[a1]*B[221]*B[1]+2*alpha*k[a1]*B[1]*B[2211]+(-alpha*R[b]*k[a1]-k[d1])*B[1]+2*B[11]*k[d1]+B[12]*k[d2]+k[d1]*B[211]+k[d2]*B[221]<br><br>(-alpha*k[a1]-alpha*k[a2])*B[2]*B[1]+alpha*k[a2]*B[2]^2+2*alpha*k[a2]*B[2]*B[22]+alpha*B[2]*B[12]*k[a2]+alpha*k[a2]*B[2]*B[211]+2*alpha*k[a2]*B[2]*B[221]+2*alpha*k[a2]*B[2]*B[2211]+(-alpha*R[b]*k[a2]-k[d2])*B[2]+B[12]*k[d1]+2*B[22]*k[d2]+k[d1]*B[211]+k[d2]*B[221]</p>
<p>the varables are the terms with B and a subsript and everything else is a parameter.</p>
<p>My intuition was to use coeffs but I couldn't get anything helpful</p><p>I am interested in the behaviour of a system of equations close to the origin- these equations are quite long, and there are a lot of them so i would like to have commands that i can use to assume products of variables are zero. </p>
<p>here are the first two polynomials:</p>
<p><br>alpha*k[a1]*B[1]^2+(-alpha*k[a1]-alpha*k[a2])*B[2]*B[1]+2*alpha*k[a1]*B[1]*B[11]+alpha*k[a1]*B[12]*B[1]+2*alpha*k[a1]*B[1]*B[211]+alpha*k[a1]*B[221]*B[1]+2*alpha*k[a1]*B[1]*B[2211]+(-alpha*R[b]*k[a1]-k[d1])*B[1]+2*B[11]*k[d1]+B[12]*k[d2]+k[d1]*B[211]+k[d2]*B[221]<br><br>(-alpha*k[a1]-alpha*k[a2])*B[2]*B[1]+alpha*k[a2]*B[2]^2+2*alpha*k[a2]*B[2]*B[22]+alpha*B[2]*B[12]*k[a2]+alpha*k[a2]*B[2]*B[211]+2*alpha*k[a2]*B[2]*B[221]+2*alpha*k[a2]*B[2]*B[2211]+(-alpha*R[b]*k[a2]-k[d2])*B[2]+B[12]*k[d1]+2*B[22]*k[d2]+k[d1]*B[211]+k[d2]*B[221]</p>
<p>the varables are the terms with B and a subsript and everything else is a parameter.</p>
<p>My intuition was to use coeffs but I couldn't get anything helpful</p>218613Tue, 04 Oct 2016 11:08:49 ZAnnonymouseAnnonymouseCoefficients extraction to form Equations
http://www.mapleprimes.com/questions/218078-Coefficients-Extraction-To-Form-Equations?ref=Feed:MaplePrimes:Tagged With coeff
<p>N := 4;<br>print(`output redirected...`); # input placeholder<br> 4<br>y := sum(A[2*n].cos(2.*n.x), n = 0 .. N);</p>
<p>eq1 := diff(y, `$`(x, 2))+(a+2*q*cos(2*x))*y</p>
<p>eq2 := map(combine, eq1, trig)</p>
<p>for i from 0 to 4 do eq4[i] := coeff(eq2, cos(2*n*x)) end do</p>
<p>From these I want to extract the co-ffficients of cos(0x),cos(2x),cos(4x)..</p>
<p>and form a simultaneous linear equation containg A0,A2,A4</p>
<p>The solution is </p>
<p>aA0+qA2=0</p>
<p>2q*A0+(a-4)*A2+q*A4=0</p>
<p>Can anybody tell me how to do it</p><p>N := 4;<br />print(`output redirected...`); # input placeholder<br /> 4<br />y := sum(A[2*n].cos(2.*n.x), n = 0 .. N);</p>
<p>eq1 := diff(y, `$`(x, 2))+(a+2*q*cos(2*x))*y</p>
<p>eq2 := map(combine, eq1, trig)</p>
<p>for i from 0 to 4 do eq4[i] := coeff(eq2, cos(2*n*x)) end do</p>
<p>From these I want to extract the co-ffficients of cos(0x),cos(2x),cos(4x)..</p>
<p>and form a simultaneous linear equation containg A0,A2,A4</p>
<p>The solution is </p>
<p>aA0+qA2=0</p>
<p>2q*A0+(a-4)*A2+q*A4=0</p>
<p>Can anybody tell me how to do it</p>218078Sat, 24 Sep 2016 08:00:40 ZRajan191Rajan191How to extract symbolic coefficient?
http://www.mapleprimes.com/questions/209926-How-To-Extract-Symbolic-Coefficient?ref=Feed:MaplePrimes:Tagged With coeff
<p>Hi dear Maple masters:</p>
<p>Excuse-me. I have a stupid question to ask: how to extract symbolic coefficient in maple? For example, I would like to get the coefficient before sin(Ωt) and cos(Ωt) in the following equation:</p>
<p>eq := (-Omega^2*a*A[2]-Omega^2*m*B[1]+Omega*A[1]*c[1]+B[1]*k[1])*cos(Omega*t)+(Omega^2*a*B[2]-Omega^2*m*A[1]-Omega*B[1]*c[1]+A[1]*k[1])*sin(Omega*t) = 0;</p>
<p>Thank you in adavance for taking a look, wish you a nice day!</p>
<p>Best regards,</p>
<p>Zihan</p><p>Hi dear Maple masters:</p>
<p>Excuse-me. I have a stupid question to ask: how to extract symbolic coefficient in maple? For example, I would like to get the coefficient before sin(Ωt) and cos(Ωt) in the following equation:</p>
<p>eq := (-Omega^2*a*A[2]-Omega^2*m*B[1]+Omega*A[1]*c[1]+B[1]*k[1])*cos(Omega*t)+(Omega^2*a*B[2]-Omega^2*m*A[1]-Omega*B[1]*c[1]+A[1]*k[1])*sin(Omega*t) = 0;</p>
<p>Thank you in adavance for taking a look, wish you a nice day!</p>
<p>Best regards,</p>
<p>Zihan</p>209926Tue, 01 Mar 2016 13:31:25 ZZihanZihanExtracting coefficients from series
http://www.mapleprimes.com/questions/209470-Extracting-Coefficients-From-Series?ref=Feed:MaplePrimes:Tagged With coeff
<p>I am trying to extract the coefficients of z from its series expansion. In two cases I succeed in finding the coefficients, but in the last one I fail to get the correct coefficients. Some garbage value is obtained. What is the reason behind this? I have attached my maple program.</p>
<p> </p>
<p> </p>
<p><a href="/view.aspx?sf=209470_question/test.mw">test.mw</a></p><p>I am trying to extract the coefficients of z from its series expansion. In two cases I succeed in finding the coefficients, but in the last one I fail to get the correct coefficients. Some garbage value is obtained. What is the reason behind this? I have attached my maple program.</p>
<p> </p>
<p> </p>
<p><a href="/view.aspx?sf=209470_question/test.mw">test.mw</a></p>209470Wed, 17 Feb 2016 05:41:10 Zlitunlitun