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http://functions.wolfram.com/09.13.16.0028.01
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Det[{{1, WeierstrassP[Subscript[z, 1], {Subscript[g, 2], Subscript[g, 3]}],
WeierstrassPPrime[Subscript[z, 1], {Subscript[g, 2], Subscript[g, 3]}]},
{1, WeierstrassP[Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}],
WeierstrassPPrime[Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}]},
{1, WeierstrassP[Subscript[z, 1] + Subscript[z, 2],
{Subscript[g, 2], Subscript[g, 3]}],
-WeierstrassPPrime[Subscript[z, 1] + Subscript[z, 2],
{Subscript[g, 2], Subscript[g, 3]}]}}] == 0
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Cell[BoxData[RowBox[List[RowBox[List["Det", "[", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["z", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], ",", RowBox[List["WeierstrassPPrime", "[", RowBox[List[SubscriptBox["z", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", ",", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["z", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], ",", RowBox[List["WeierstrassPPrime", "[", RowBox[List[SubscriptBox["z", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", ",", RowBox[List["WeierstrassP", "[", RowBox[List[RowBox[List[SubscriptBox["z", "1"], "+", SubscriptBox["z", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], ",", RowBox[List["-", RowBox[List["WeierstrassPPrime", "[", RowBox[List[RowBox[List[SubscriptBox["z", "1"], "+", SubscriptBox["z", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]]]], "}"]]]], "}"]], "]"]], "\[Equal]", "0"]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mo> ❘ </mo> <mtext> ⁠ </mtext> <mtable> <mtr> <mtd> <mn> 1 </mn> </mtd> <mtd> <mrow> <mi> ℘ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msup> <mi> ℘ </mi> <mo> ′ </mo> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn> 1 </mn> </mtd> <mtd> <mrow> <mi> ℘ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msup> <mi> ℘ </mi> <mo> ′ </mo> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn> 1 </mn> </mtd> <mtd> <mrow> <mi> ℘ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mrow> <mo> - </mo> <msup> <mi> ℘ </mi> <mo> ′ </mo> </msup> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mtext> ⁠ </mtext> <mo> ❘ </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[LeftBracketingBar]", "\[NoBreak]", GridBox[List[List["1", RowBox[List["\[WeierstrassP]", RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["z", "1"], ";", SubscriptBox["g", "2"]]], ",", SubscriptBox["g", "3"]]], ")"]]]], RowBox[List[SuperscriptBox["\[WeierstrassP]", "\[Prime]"], RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["z", "1"], ";", SubscriptBox["g", "2"]]], ",", SubscriptBox["g", "3"]]], ")"]]]]], List["1", RowBox[List["\[WeierstrassP]", RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["z", "2"], ";", SubscriptBox["g", "2"]]], ",", SubscriptBox["g", "3"]]], ")"]]]], RowBox[List[SuperscriptBox["\[WeierstrassP]", "\[Prime]"], RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["z", "2"], ";", SubscriptBox["g", "2"]]], ",", SubscriptBox["g", "3"]]], ")"]]]]], List["1", RowBox[List["\[WeierstrassP]", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["z", "1"], "+", SubscriptBox["z", "2"]]], ";", SubscriptBox["g", "2"]]], ",", SubscriptBox["g", "3"]]], ")"]]]], RowBox[List[RowBox[List["-", SuperscriptBox["\[WeierstrassP]", "\[Prime]"]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["z", "1"], "+", SubscriptBox["z", "2"]]], ";", SubscriptBox["g", "2"]]], ",", SubscriptBox["g", "3"]]], ")"]]]]]]], "\[NoBreak]", "\[RightBracketingBar]"]], List[Det]] </annotation> </semantics> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <semantics> <mrow> <mo> ❘ </mo> <mtext> ⁠ </mtext> <mtable> <mtr> <mtd> <mn> 1 </mn> </mtd> <mtd> <mrow> <mi> ℘ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msup> <mi> ℘ </mi> <mo> ′ </mo> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn> 1 </mn> </mtd> <mtd> <mrow> <mi> ℘ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msup> <mi> ℘ </mi> <mo> ′ </mo> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn> 1 </mn> </mtd> <mtd> <mrow> <mi> ℘ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mrow> <mo> - </mo> <msup> <mi> ℘ </mi> <mo> ′ </mo> </msup> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mtext> ⁠ </mtext> <mo> ❘ </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[LeftBracketingBar]", "\[NoBreak]", GridBox[List[List["1", RowBox[List["\[WeierstrassP]", RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["z", "1"], ";", SubscriptBox["g", "2"]]], ",", SubscriptBox["g", "3"]]], ")"]]]], RowBox[List[SuperscriptBox["\[WeierstrassP]", "\[Prime]"], RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["z", "1"], ";", SubscriptBox["g", "2"]]], ",", SubscriptBox["g", "3"]]], ")"]]]]], List["1", RowBox[List["\[WeierstrassP]", RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["z", "2"], ";", SubscriptBox["g", "2"]]], ",", SubscriptBox["g", "3"]]], ")"]]]], RowBox[List[SuperscriptBox["\[WeierstrassP]", "\[Prime]"], RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["z", "2"], ";", SubscriptBox["g", "2"]]], ",", SubscriptBox["g", "3"]]], ")"]]]]], List["1", RowBox[List["\[WeierstrassP]", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["z", "1"], "+", SubscriptBox["z", "2"]]], ";", SubscriptBox["g", "2"]]], ",", SubscriptBox["g", "3"]]], ")"]]]], RowBox[List[RowBox[List["-", SuperscriptBox["\[WeierstrassP]", "\[Prime]"]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["z", "1"], "+", SubscriptBox["z", "2"]]], ";", SubscriptBox["g", "2"]]], ",", SubscriptBox["g", "3"]]], ")"]]]]]]], "\[NoBreak]", "\[RightBracketingBar]"]], List[Det]] </annotation> </semantics> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Det", "[", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["z_", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], ",", RowBox[List["WeierstrassPPrime", "[", RowBox[List[SubscriptBox["z_", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", ",", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["z_", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], ",", RowBox[List["WeierstrassPPrime", "[", RowBox[List[SubscriptBox["z_", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", ",", RowBox[List["WeierstrassP", "[", RowBox[List[RowBox[List[SubscriptBox["z_", "1"], "+", SubscriptBox["z_", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], ",", RowBox[List["-", RowBox[List["WeierstrassPPrime", "[", RowBox[List[RowBox[List[SubscriptBox["z_", "1"], "+", SubscriptBox["z_", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]]]], "}"]]]], "}"]], "]"]], "]"]], "\[RuleDelayed]", "0"]]]] |
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Date Added to functions.wolfram.com (modification date)
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