Solve Polynomial and transcendental Equations with use Generalized Theorem (Method Lagrange)
Author
Nikos Mantzakouras
Title
Solve Polynomial and transcendental Equations with use Generalized Theorem (Method Lagrange)
Description
General method for solving Transcendental & Polynomial equations and systems with the new Generalized Theorem with 2 methods (Lagrange and the second one, exists in application, but will be published later).Because this project is a small sample of work, the work can be extended to a large extent, and is compatible with the mathematica program. Clearly I would like a cooperation only with mathematica because I think it is the best program in the world ,but also I believe you could make better use of the theory behind and the examples that cover many applications.If you want cooperation and professional I will wait for your answer and offer. Thank you I wish the best to your company.
Category
Working Material
Keywords
Transcendental equations, solution, Hypergeometric functions, field-subfield of roots, Polynomial, famus equations
URL
http://www.notebookarchive.org/2021-08-5izzhlh/
DOI
https://notebookarchive.org/2021-08-5izzhlh
Date Added
2021-08-12
Date Last Modified
2021-08-12
File Size
57.68 kilobytes
Supplements
Rights
Redistribution rights reserved
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....................................................................Programforsolvingofthetrigonometricexponentialequationofmyfile{s*Sin(x)+m*Exp(x)+t=0}'d=IntervalValues,k=CountofLoop,{m,s,tcoefficientsoftheequation}''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
Program1'ComplexRoots
In[]:=
ClearAll;Off[General::munfl,FindRoot::lstol,FindRoot::cvmit,FindRoot::bddir];d:=10;s:=1/2;m:=-15;q:=15;t:=π;h[x_]:=s*Sin[x]+m*Exp[x]+t;Fork=-d,k<-1,k++,xr=N[π-ArcSin[x]+2*k*π]+NGamma[w+1]*D[-ArcSin[x]*,{x,w-1}];FQ2=N[xr/.x-t/s];Column[Print["Approach=",N[h[y]]/.FindRoot[h[y]0,{y,FQ2},WorkingPrecision10],"x(",k,")=",N[y]/.FindRoot[h[y]0,{y,FQ2},WorkingPrecision20]]]
q
∑
w=1
w
(-m/s)
∂
x
w
(Exp[π-ArcSin[x]+2*k*π])
Approach=0.+4.98284×x(-10)=-58.119464091411174912-2.5246306599334671361
-25
10
Approach=0.+2.66827×x(-9)=-51.836278784231588435-2.5246306599334671361
-22
10
Approach=0.+1.42884×x(-8)=-45.553093477052001958-2.5246306599334671361
-19
10
Approach=0.+7.6513×x(-7)=-39.269908169872415456-2.5246306599334671361
-17
10
Approach=0.+4.09721×x(-6)=-32.986722862692815794-2.5246306599334857879
-14
10
Approach=0.+2.19402×x(-5)=-26.703537555506168577-2.5246306599434398898
-11
10
Approach=0.+1.0392×x(-4)=-20.420352244545614887-2.5246306652737568232
-19
10
Approach=0.+1.63477×x(-3)=-14.137164912699556237-2.5246335196235255250
-19
10
Approach=0.+4.33681×x(-2)=-7.8528982682336170186-2.5261647240710902859
-19
10
Program2'(RealRoot)
In[]:=
Off[General::munfl,FindRoot::lstol];d:=1;s:=1/2;m:=-15;q:=15;t:=π;h[x_]:=s*Sin[x]+m*Exp[x]+t;Fork1=0,k1<1,k1++,xr=N[Log[x1]2*k1*π*I]+N(/Gamma[w+1])*D[1/x1*,{x1,w-1}];FQ2=N[xr/.x1-t/m];Column[Print["Approach=",N[h[y],30]/.FindRoot[h[y]0,{y,FQ2},WorkingPrecision30],"x(",k,")=",N[y]/.FindRoot[h[y]0,{y,FQ2},WorkingPrecision30]]]
q
∑
w=1
w
(-s/m)
w
(Sin[Log[x1]+2*k1*π*I])
Approach=0.×x(-1)=-1.73415151127437752804203156842
-29
10
In[]:=
Plot[-s*Sin[FQ]-m*Exp[FQ]+t,{FQ,-20,5}]
Out[]=
Program3.'SecondgroupofComplexRoots(Conjugatedcomplexroots)'
In[]:=
ClearAll;Off[General::munfl,FindRoot::lstol,FindRoot::bddir];d:=10;s:=1/2;m:=-15;q:=15;t:=π;h[x_]:=s*Sin[x]+m*Exp[x]+t;Fork=-d,k≤-1,k++,xr=N[ArcSin[x]+2*k*π]+NGamma[w+1]*D[ArcSin[x]*,{x,w-1}];FQ2=N[xr/.x-t/s];Column[Print["Approach=",N[h[y],15]/.FindRoot[h[y]0,{y,FQ2},WorkingPrecision30],"x(",k,")=",N[y]/.FindRoot[h[y]0,{y,FQ2},WorkingPrecision15]]]
q
∑
w=1
w
(-m/s)
∂
x
w
(Exp[ArcSin[x]+2*k*π])
Approach=0.×+0.×x(-10)=-64.4026493985908+2.52463065993347
-15
10
-28
10
Approach=0.×+0.×x(-9)=-58.1194640914112+2.52463065993347
-15
10
-28
10
Approach=0.×+0.×x(-8)=-51.8362787842316+2.52463065993347
-15
10
-28
10
Approach=0.×-2.062682219×x(-7)=-45.5530934770520+2.52463065993347
-15
10
-18
10
Approach=0.×+0.×x(-6)=-39.2699081698724+2.52463065993347
-15
10
-28
10
Approach=0.×+0.×x(-5)=-32.9867228626928+2.52463065993349
-15
10
-27
10
Approach=0.×+0.×x(-4)=-26.7035375555062+2.52463065994344
-15
10
-25
10
Approach=0.×+0.×x(-3)=-20.4203522445456+2.52463066527376
-15
10
-22
10
Approach=0.×+0.×x(-2)=-14.1371649126996+2.52463351962353
-15
10
-19
10
Approach=0.×+0.×x(-1)=-7.85289826823362+2.52616472407109
-15
10
-17
10
Cite this as: Nikos Mantzakouras, "Solve Polynomial and transcendental Equations with use Generalized Theorem (Method Lagrange)" from the Notebook Archive (2021), https://notebookarchive.org/2021-08-5izzhlh
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