Reconstructing a polynomial from its coefficient array

2

$begingroup$

A polynomial coefficient matrix:

mat = 

  CoefficientList[3 + 5 x^3 + 4 y^3 + 2 x + 6 x^2 y + 7 x y^2 + 8 x y, {x, y}]; 

begin{equation}
left(
begin{array}{cccc}
3 & 0 & 0 & 4 \
2 & 8 & 7 & 0 \
0 & 6 & 0 & 0 \
5 & 0 & 0 & 0 \
end{array}
right)
end{equation}

Another matrix:

list = 

  {{a1, b1, c1, d1}, {e1, f1, g1, h1}, {i1, j1, k1, l1}, {m1, n1,o1, p1}};

whose matrix form is:
begin{equation}
left(
begin{array}{cccc}
a1 & b1 & c1 & d1 \
e1 & f1 & g1 & h1 \
i1 & j1 & k1 & l1 \
m1 & n1 & o1 & p1 \
end{array}
right)
end{equation}

How can I generate the following polynomial automatically?

$text{a1}+text{d1} y^3+text{e1} x+text{f1} x y+text{g1} x y^2+text{j1} x^2 y+text{m1} x^3$

list-manipulation algebraic-manipulation

share|improve this question

edited Jan 13 at 1:25

m_goldberg

86k872196

asked Jan 13 at 0:38

Chandan SharmaChandan Sharma

1246

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Why are some entries of the matrix ignored? Maybe this, if that is a mistake: {{a1, b1, c1, d1}, {e1, f1, g1, h1}, {i1, j1, k1, l1}, {m1, n1, o1, p1}}.y^Range[0, 3].x^Range[0, 3]
  $endgroup$
  – Michael E2
  Jan 13 at 0:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  There's an example in the docs for CoefficientList for how to recover the polynomial from the matrix: Look for Fold[FromDigits[Reverse[#1], #2] &, %, {x, y}].
  $endgroup$
  – Michael E2
  Jan 13 at 0:42
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @MichaelE2 I am ignoring only those entries for which the constant is zero as in coefficientlist matrix.
  $endgroup$
  – Chandan Sharma
  Jan 13 at 0:48
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Do you mean Fold[FromDigits[Reverse[#1], #2] &, Unitize@mat * list, {x, y}]?
  $endgroup$
  – Michael E2
  Jan 13 at 1:43
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @MichaelE2 Exactly.
  $endgroup$
  – Chandan Sharma
  Jan 13 at 1:53
  

  
  
  
  

 | 
show 1 more comment

2

$begingroup$

A polynomial coefficient matrix:

mat = 

  CoefficientList[3 + 5 x^3 + 4 y^3 + 2 x + 6 x^2 y + 7 x y^2 + 8 x y, {x, y}]; 

begin{equation}
left(
begin{array}{cccc}
3 & 0 & 0 & 4 \
2 & 8 & 7 & 0 \
0 & 6 & 0 & 0 \
5 & 0 & 0 & 0 \
end{array}
right)
end{equation}

Another matrix:

list = 

  {{a1, b1, c1, d1}, {e1, f1, g1, h1}, {i1, j1, k1, l1}, {m1, n1,o1, p1}};

whose matrix form is:
begin{equation}
left(
begin{array}{cccc}
a1 & b1 & c1 & d1 \
e1 & f1 & g1 & h1 \
i1 & j1 & k1 & l1 \
m1 & n1 & o1 & p1 \
end{array}
right)
end{equation}

How can I generate the following polynomial automatically?

$text{a1}+text{d1} y^3+text{e1} x+text{f1} x y+text{g1} x y^2+text{j1} x^2 y+text{m1} x^3$

list-manipulation algebraic-manipulation

share|improve this question

edited Jan 13 at 1:25

m_goldberg

86k872196

asked Jan 13 at 0:38

Chandan SharmaChandan Sharma

1246

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Why are some entries of the matrix ignored? Maybe this, if that is a mistake: {{a1, b1, c1, d1}, {e1, f1, g1, h1}, {i1, j1, k1, l1}, {m1, n1, o1, p1}}.y^Range[0, 3].x^Range[0, 3]
  $endgroup$
  – Michael E2
  Jan 13 at 0:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  There's an example in the docs for CoefficientList for how to recover the polynomial from the matrix: Look for Fold[FromDigits[Reverse[#1], #2] &, %, {x, y}].
  $endgroup$
  – Michael E2
  Jan 13 at 0:42
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @MichaelE2 I am ignoring only those entries for which the constant is zero as in coefficientlist matrix.
  $endgroup$
  – Chandan Sharma
  Jan 13 at 0:48
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Do you mean Fold[FromDigits[Reverse[#1], #2] &, Unitize@mat * list, {x, y}]?
  $endgroup$
  – Michael E2
  Jan 13 at 1:43
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @MichaelE2 Exactly.
  $endgroup$
  – Chandan Sharma
  Jan 13 at 1:53
  

  
  
  
  

 | 
show 1 more comment

2

2

2

$begingroup$

A polynomial coefficient matrix:

mat = 

  CoefficientList[3 + 5 x^3 + 4 y^3 + 2 x + 6 x^2 y + 7 x y^2 + 8 x y, {x, y}]; 

begin{equation}
left(
begin{array}{cccc}
3 & 0 & 0 & 4 \
2 & 8 & 7 & 0 \
0 & 6 & 0 & 0 \
5 & 0 & 0 & 0 \
end{array}
right)
end{equation}

Another matrix:

list = 

  {{a1, b1, c1, d1}, {e1, f1, g1, h1}, {i1, j1, k1, l1}, {m1, n1,o1, p1}};

whose matrix form is:
begin{equation}
left(
begin{array}{cccc}
a1 & b1 & c1 & d1 \
e1 & f1 & g1 & h1 \
i1 & j1 & k1 & l1 \
m1 & n1 & o1 & p1 \
end{array}
right)
end{equation}

How can I generate the following polynomial automatically?

$text{a1}+text{d1} y^3+text{e1} x+text{f1} x y+text{g1} x y^2+text{j1} x^2 y+text{m1} x^3$

list-manipulation algebraic-manipulation

share|improve this question

edited Jan 13 at 1:25

m_goldberg

86k872196

asked Jan 13 at 0:38

Chandan SharmaChandan Sharma

1246

$endgroup$

A polynomial coefficient matrix:

mat = 

  CoefficientList[3 + 5 x^3 + 4 y^3 + 2 x + 6 x^2 y + 7 x y^2 + 8 x y, {x, y}]; 

begin{equation}
left(
begin{array}{cccc}
3 & 0 & 0 & 4 \
2 & 8 & 7 & 0 \
0 & 6 & 0 & 0 \
5 & 0 & 0 & 0 \
end{array}
right)
end{equation}

Another matrix:

list = 

  {{a1, b1, c1, d1}, {e1, f1, g1, h1}, {i1, j1, k1, l1}, {m1, n1,o1, p1}};

whose matrix form is:
begin{equation}
left(
begin{array}{cccc}
a1 & b1 & c1 & d1 \
e1 & f1 & g1 & h1 \
i1 & j1 & k1 & l1 \
m1 & n1 & o1 & p1 \
end{array}
right)
end{equation}

How can I generate the following polynomial automatically?

$text{a1}+text{d1} y^3+text{e1} x+text{f1} x y+text{g1} x y^2+text{j1} x^2 y+text{m1} x^3$

list-manipulation algebraic-manipulation

list-manipulation algebraic-manipulation

share|improve this question

edited Jan 13 at 1:25

m_goldberg

86k872196

asked Jan 13 at 0:38

Chandan SharmaChandan Sharma

1246

share|improve this question

edited Jan 13 at 1:25

m_goldberg

86k872196

asked Jan 13 at 0:38

Chandan SharmaChandan Sharma

1246

share|improve this question

share|improve this question

edited Jan 13 at 1:25

m_goldberg

86k872196

edited Jan 13 at 1:25

m_goldberg

86k872196

edited Jan 13 at 1:25

m_goldberg

86k872196

86k872196

asked Jan 13 at 0:38

Chandan SharmaChandan Sharma

1246

asked Jan 13 at 0:38

Chandan SharmaChandan Sharma

1246

asked Jan 13 at 0:38

Chandan SharmaChandan Sharma

1246

1246

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Why are some entries of the matrix ignored? Maybe this, if that is a mistake: {{a1, b1, c1, d1}, {e1, f1, g1, h1}, {i1, j1, k1, l1}, {m1, n1, o1, p1}}.y^Range[0, 3].x^Range[0, 3]
  $endgroup$
  – Michael E2
  Jan 13 at 0:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  There's an example in the docs for CoefficientList for how to recover the polynomial from the matrix: Look for Fold[FromDigits[Reverse[#1], #2] &, %, {x, y}].
  $endgroup$
  – Michael E2
  Jan 13 at 0:42
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @MichaelE2 I am ignoring only those entries for which the constant is zero as in coefficientlist matrix.
  $endgroup$
  – Chandan Sharma
  Jan 13 at 0:48
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Do you mean Fold[FromDigits[Reverse[#1], #2] &, Unitize@mat * list, {x, y}]?
  $endgroup$
  – Michael E2
  Jan 13 at 1:43
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @MichaelE2 Exactly.
  $endgroup$
  – Chandan Sharma
  Jan 13 at 1:53
  

  
  
  
  

 | 
show 1 more comment

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Why are some entries of the matrix ignored? Maybe this, if that is a mistake: {{a1, b1, c1, d1}, {e1, f1, g1, h1}, {i1, j1, k1, l1}, {m1, n1, o1, p1}}.y^Range[0, 3].x^Range[0, 3]
  $endgroup$
  – Michael E2
  Jan 13 at 0:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  There's an example in the docs for CoefficientList for how to recover the polynomial from the matrix: Look for Fold[FromDigits[Reverse[#1], #2] &, %, {x, y}].
  $endgroup$
  – Michael E2
  Jan 13 at 0:42
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @MichaelE2 I am ignoring only those entries for which the constant is zero as in coefficientlist matrix.
  $endgroup$
  – Chandan Sharma
  Jan 13 at 0:48
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Do you mean Fold[FromDigits[Reverse[#1], #2] &, Unitize@mat * list, {x, y}]?
  $endgroup$
  – Michael E2
  Jan 13 at 1:43
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @MichaelE2 Exactly.
  $endgroup$
  – Chandan Sharma
  Jan 13 at 1:53
  

  
  
  
  

1

1

$begingroup$
Why are some entries of the matrix ignored? Maybe this, if that is a mistake: {{a1, b1, c1, d1}, {e1, f1, g1, h1}, {i1, j1, k1, l1}, {m1, n1, o1, p1}}.y^Range[0, 3].x^Range[0, 3]
$endgroup$
– Michael E2
Jan 13 at 0:41

$begingroup$
Why are some entries of the matrix ignored? Maybe this, if that is a mistake: {{a1, b1, c1, d1}, {e1, f1, g1, h1}, {i1, j1, k1, l1}, {m1, n1, o1, p1}}.y^Range[0, 3].x^Range[0, 3]
$endgroup$
– Michael E2
Jan 13 at 0:41

$begingroup$
There's an example in the docs for CoefficientList for how to recover the polynomial from the matrix: Look for Fold[FromDigits[Reverse[#1], #2] &, %, {x, y}].
$endgroup$
– Michael E2
Jan 13 at 0:42

$begingroup$
There's an example in the docs for CoefficientList for how to recover the polynomial from the matrix: Look for Fold[FromDigits[Reverse[#1], #2] &, %, {x, y}].
$endgroup$
– Michael E2
Jan 13 at 0:42

$begingroup$
@MichaelE2 I am ignoring only those entries for which the constant is zero as in coefficientlist matrix.
$endgroup$
– Chandan Sharma
Jan 13 at 0:48

$begingroup$
@MichaelE2 I am ignoring only those entries for which the constant is zero as in coefficientlist matrix.
$endgroup$
– Chandan Sharma
Jan 13 at 0:48

1

1

$begingroup$
Do you mean Fold[FromDigits[Reverse[#1], #2] &, Unitize@mat * list, {x, y}]?
$endgroup$
– Michael E2
Jan 13 at 1:43

$begingroup$
Do you mean Fold[FromDigits[Reverse[#1], #2] &, Unitize@mat * list, {x, y}]?
$endgroup$
– Michael E2
Jan 13 at 1:43

$begingroup$
@MichaelE2 Exactly.
$endgroup$
– Chandan Sharma
Jan 13 at 1:53

$begingroup$
@MichaelE2 Exactly.
$endgroup$
– Chandan Sharma
Jan 13 at 1:53

 | 
show 1 more comment

5 Answers
5

active

oldest

votes

2

$begingroup$

Using mat as the template:

Plus @@ Flatten[Table[If[mat[[i, j]] == 0, 0, list[[i, j]] x^(i - 1) y^(j - 1)], 

   {i, 1, 4}, {j, 1, 4}]]

(* a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3 *)

share|improve this answer

answered Jan 13 at 1:35

John DotyJohn Doty

6,95811024

$endgroup$

add a comment | 

7

$begingroup$

Internal`FromCoefficientList[mat, {x, y}]

3 + 2 x + 5 x^3 + 8 x y + 6 x^2 y + 7 x y^2 + 4 y^3

Internal`FromCoefficientList[list Unitize[mat], {x, y}]

a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3

share|improve this answer

answered Jan 13 at 2:41

kglrkglr

183k10201416

$endgroup$

add a comment | 

3

$begingroup$

Adapting an example from the documentation for CoefficientList:

Fold[FromDigits[Reverse[#1], #2] &, Unitize@mat*list, {x, y}]

(*  a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3  *)

share|improve this answer

answered Jan 13 at 2:08

Michael E2Michael E2

147k12197473

$endgroup$

add a comment | 

3

$begingroup$

Terse:

Total[Array[x^# y^#2 &, {4, 4}, 0] list Unitize@mat, 2]

a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3

share|improve this answer

answered Jan 13 at 4:21

Mr.Wizard♦Mr.Wizard

231k294761046

$endgroup$

add a comment | 

2

$begingroup$

You will have to tell Mathematica where the zero coefficients are, but if you do that it can be done like so:

list = {{a1, 0, 0, d1}, {e1, f1, g1, 0}, {0, 0, 0, l1}, {m1, 0, 0, 0}}; 

Fold[FromDigits[Reverse[#1], #2] &, list, {x, y}] // Expand

a1 + e1 x + m1 x^3 + f1 x y + g1 x y^2 + d1 y^3 + l1 x^2 y^3

This is discussed in the documentation of CoefficientList in the section Properties & Relations.

share|improve this answer

answered Jan 13 at 1:14

m_goldbergm_goldberg

86k872196

$endgroup$

add a comment | 

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5 Answers
5

active

oldest

votes

5 Answers
5

active

oldest

votes

active

oldest

votes

active

oldest

votes

2

$begingroup$

Using mat as the template:

Plus @@ Flatten[Table[If[mat[[i, j]] == 0, 0, list[[i, j]] x^(i - 1) y^(j - 1)], 

   {i, 1, 4}, {j, 1, 4}]]

(* a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3 *)

share|improve this answer

answered Jan 13 at 1:35

John DotyJohn Doty

6,95811024

$endgroup$

add a comment | 

2

$begingroup$

Using mat as the template:

Plus @@ Flatten[Table[If[mat[[i, j]] == 0, 0, list[[i, j]] x^(i - 1) y^(j - 1)], 

   {i, 1, 4}, {j, 1, 4}]]

(* a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3 *)

share|improve this answer

answered Jan 13 at 1:35

John DotyJohn Doty

6,95811024

$endgroup$

add a comment | 

2

2

2

$begingroup$

Using mat as the template:

Plus @@ Flatten[Table[If[mat[[i, j]] == 0, 0, list[[i, j]] x^(i - 1) y^(j - 1)], 

   {i, 1, 4}, {j, 1, 4}]]

(* a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3 *)

share|improve this answer

answered Jan 13 at 1:35

John DotyJohn Doty

6,95811024

$endgroup$

Using mat as the template:

Plus @@ Flatten[Table[If[mat[[i, j]] == 0, 0, list[[i, j]] x^(i - 1) y^(j - 1)], 

   {i, 1, 4}, {j, 1, 4}]]

(* a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3 *)

share|improve this answer

answered Jan 13 at 1:35

John DotyJohn Doty

6,95811024

share|improve this answer

share|improve this answer

answered Jan 13 at 1:35

John DotyJohn Doty

6,95811024

answered Jan 13 at 1:35

John DotyJohn Doty

6,95811024

answered Jan 13 at 1:35

John DotyJohn Doty

6,95811024

6,95811024

add a comment | 

add a comment | 

7

$begingroup$

Internal`FromCoefficientList[mat, {x, y}]

3 + 2 x + 5 x^3 + 8 x y + 6 x^2 y + 7 x y^2 + 4 y^3

Internal`FromCoefficientList[list Unitize[mat], {x, y}]

a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3

share|improve this answer

answered Jan 13 at 2:41

kglrkglr

183k10201416

$endgroup$

add a comment | 

7

$begingroup$

Internal`FromCoefficientList[mat, {x, y}]

3 + 2 x + 5 x^3 + 8 x y + 6 x^2 y + 7 x y^2 + 4 y^3

Internal`FromCoefficientList[list Unitize[mat], {x, y}]

a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3

share|improve this answer

answered Jan 13 at 2:41

kglrkglr

183k10201416

$endgroup$

add a comment | 

7

7

7

$begingroup$

Internal`FromCoefficientList[mat, {x, y}]

3 + 2 x + 5 x^3 + 8 x y + 6 x^2 y + 7 x y^2 + 4 y^3

Internal`FromCoefficientList[list Unitize[mat], {x, y}]

a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3

share|improve this answer

answered Jan 13 at 2:41

kglrkglr

183k10201416

$endgroup$

Internal`FromCoefficientList[mat, {x, y}]

3 + 2 x + 5 x^3 + 8 x y + 6 x^2 y + 7 x y^2 + 4 y^3

Internal`FromCoefficientList[list Unitize[mat], {x, y}]

a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3

share|improve this answer

answered Jan 13 at 2:41

kglrkglr

183k10201416

share|improve this answer

share|improve this answer

answered Jan 13 at 2:41

kglrkglr

183k10201416

answered Jan 13 at 2:41

kglrkglr

183k10201416

answered Jan 13 at 2:41

kglrkglr

183k10201416

183k10201416

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3

$begingroup$

Adapting an example from the documentation for CoefficientList:

Fold[FromDigits[Reverse[#1], #2] &, Unitize@mat*list, {x, y}]

(*  a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3  *)

share|improve this answer

answered Jan 13 at 2:08

Michael E2Michael E2

147k12197473

$endgroup$

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3

$begingroup$

Adapting an example from the documentation for CoefficientList:

Fold[FromDigits[Reverse[#1], #2] &, Unitize@mat*list, {x, y}]

(*  a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3  *)

share|improve this answer

answered Jan 13 at 2:08

Michael E2Michael E2

147k12197473

$endgroup$

add a comment | 

3

3

3

$begingroup$

Adapting an example from the documentation for CoefficientList:

Fold[FromDigits[Reverse[#1], #2] &, Unitize@mat*list, {x, y}]

(*  a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3  *)

share|improve this answer

answered Jan 13 at 2:08

Michael E2Michael E2

147k12197473

$endgroup$

Adapting an example from the documentation for CoefficientList:

Fold[FromDigits[Reverse[#1], #2] &, Unitize@mat*list, {x, y}]

(*  a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3  *)

share|improve this answer

answered Jan 13 at 2:08

Michael E2Michael E2

147k12197473

share|improve this answer

share|improve this answer

answered Jan 13 at 2:08

Michael E2Michael E2

147k12197473

answered Jan 13 at 2:08

Michael E2Michael E2

147k12197473

answered Jan 13 at 2:08

Michael E2Michael E2

147k12197473

147k12197473

add a comment | 

add a comment | 

3

$begingroup$

Terse:

Total[Array[x^# y^#2 &, {4, 4}, 0] list Unitize@mat, 2]

a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3

share|improve this answer

answered Jan 13 at 4:21

Mr.Wizard♦Mr.Wizard

231k294761046

$endgroup$

add a comment | 

3

$begingroup$

Terse:

Total[Array[x^# y^#2 &, {4, 4}, 0] list Unitize@mat, 2]

a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3

share|improve this answer

answered Jan 13 at 4:21

Mr.Wizard♦Mr.Wizard

231k294761046

$endgroup$

add a comment | 

3

3

3

$begingroup$

Terse:

Total[Array[x^# y^#2 &, {4, 4}, 0] list Unitize@mat, 2]

a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3

share|improve this answer

answered Jan 13 at 4:21

Mr.Wizard♦Mr.Wizard

231k294761046

$endgroup$

Terse:

Total[Array[x^# y^#2 &, {4, 4}, 0] list Unitize@mat, 2]

a1 + e1 x + m1 x^3 + f1 x y + j1 x^2 y + g1 x y^2 + d1 y^3

share|improve this answer

answered Jan 13 at 4:21

Mr.Wizard♦Mr.Wizard

231k294761046

share|improve this answer

share|improve this answer

answered Jan 13 at 4:21

Mr.Wizard♦Mr.Wizard

231k294761046

answered Jan 13 at 4:21

Mr.Wizard♦Mr.Wizard

231k294761046

answered Jan 13 at 4:21

Mr.Wizard♦Mr.Wizard

231k294761046

231k294761046

add a comment | 

add a comment | 

2

$begingroup$

You will have to tell Mathematica where the zero coefficients are, but if you do that it can be done like so:

list = {{a1, 0, 0, d1}, {e1, f1, g1, 0}, {0, 0, 0, l1}, {m1, 0, 0, 0}}; 

Fold[FromDigits[Reverse[#1], #2] &, list, {x, y}] // Expand

a1 + e1 x + m1 x^3 + f1 x y + g1 x y^2 + d1 y^3 + l1 x^2 y^3

This is discussed in the documentation of CoefficientList in the section Properties & Relations.

share|improve this answer

answered Jan 13 at 1:14

m_goldbergm_goldberg

86k872196

$endgroup$

add a comment | 

2

$begingroup$

You will have to tell Mathematica where the zero coefficients are, but if you do that it can be done like so:

list = {{a1, 0, 0, d1}, {e1, f1, g1, 0}, {0, 0, 0, l1}, {m1, 0, 0, 0}}; 

Fold[FromDigits[Reverse[#1], #2] &, list, {x, y}] // Expand

a1 + e1 x + m1 x^3 + f1 x y + g1 x y^2 + d1 y^3 + l1 x^2 y^3

This is discussed in the documentation of CoefficientList in the section Properties & Relations.

share|improve this answer

answered Jan 13 at 1:14

m_goldbergm_goldberg

86k872196

$endgroup$

add a comment | 

2

2

2

$begingroup$

You will have to tell Mathematica where the zero coefficients are, but if you do that it can be done like so:

list = {{a1, 0, 0, d1}, {e1, f1, g1, 0}, {0, 0, 0, l1}, {m1, 0, 0, 0}}; 

Fold[FromDigits[Reverse[#1], #2] &, list, {x, y}] // Expand

a1 + e1 x + m1 x^3 + f1 x y + g1 x y^2 + d1 y^3 + l1 x^2 y^3

This is discussed in the documentation of CoefficientList in the section Properties & Relations.

share|improve this answer

answered Jan 13 at 1:14

m_goldbergm_goldberg

86k872196

$endgroup$

You will have to tell Mathematica where the zero coefficients are, but if you do that it can be done like so:

list = {{a1, 0, 0, d1}, {e1, f1, g1, 0}, {0, 0, 0, l1}, {m1, 0, 0, 0}}; 

Fold[FromDigits[Reverse[#1], #2] &, list, {x, y}] // Expand

a1 + e1 x + m1 x^3 + f1 x y + g1 x y^2 + d1 y^3 + l1 x^2 y^3

This is discussed in the documentation of CoefficientList in the section Properties & Relations.

share|improve this answer

answered Jan 13 at 1:14

m_goldbergm_goldberg

86k872196

share|improve this answer

share|improve this answer

answered Jan 13 at 1:14

m_goldbergm_goldberg

86k872196

answered Jan 13 at 1:14

m_goldbergm_goldberg

86k872196

answered Jan 13 at 1:14

m_goldbergm_goldberg

86k872196

86k872196

add a comment | 

add a comment | 

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