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No commits in common. "2761a3b3ee84186f890893884849ef7c1e6c9988" and "2212957562b08fe6cbd4ab96b8cb21883abd8bea" have entirely different histories.
2761a3b3ee
...
2212957562
@ -5,23 +5,7 @@
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"execution_count": 1,
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"id": "72d5a30c-1a59-4a55-9680-fdfa7979625b",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<html>\\(\\displaystyle z^{3} - 3 y^{2} z + 3 x^{2} z + 2 x^{4}\\)</html>"
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],
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"text/latex": [
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"$\\displaystyle z^{3} - 3 y^{2} z + 3 x^{2} z + 2 x^{4}$"
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],
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"text/plain": [
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"z^3 - 3*y^2*z + 3*x^2*z + 2*x^4"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"outputs": [],
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"source": [
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"# load('zetas_triples_general.py')\n",
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"R.<x, y, z> = PolynomialRing(QQ, order='neglex')\n",
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@ -29,8 +13,7 @@
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"f = v^2 - u^2\n",
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"g = u^4\n",
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"F = z^3 - 3 * f(u=x, v=y) * z + 2 * g(u=x, v=y)\n",
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"h = F.discriminant(z)(x=u, y=v)\n",
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"show(F)"
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"h = F.discriminant(z)(x=u, y=v)"
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]
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},
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{
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@ -89,21 +72,6 @@
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"id": "27e92ddc-34d6-4290-880f-9d3561a8ec4e",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<html>\\(\\displaystyle z^{3} - 3 y^{2} z + t x z^{2} + 3 x^{2} z + 2 x^{4}\\)</html>"
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],
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"text/latex": [
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"$\\displaystyle z^{3} - 3 y^{2} z + t x z^{2} + 3 x^{2} z + 2 x^{4}$"
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],
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"text/plain": [
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"z^3 - 3*y^2*z + t*x*z^2 + 3*x^2*z + 2*x^4"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/plain": [
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@ -117,40 +85,12 @@
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],
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"source": [
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"Ft = F + t * x * z^2\n",
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"show(Ft)\n",
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"Ft.jacobian_ideal().vector_space_dimension()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"id": "83328b3a-8da8-4adc-8b6c-02764b1420d3",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<html>\\(\\displaystyle 108 y^{6} + \\left(9 t^{2} - 324\\right) x^{2} y^{4} + \\left(-18 t^{2} + 324\\right) x^{4} y^{2} - 108 t x^{5} y^{2} + \\left(9 t^{2} - 108\\right) x^{6} + \\left(-8 t^{3} + 108 t\\right) x^{7} - 108 x^{8}\\)</html>"
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],
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"text/latex": [
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"$\\displaystyle 108 y^{6} + \\left(9 t^{2} - 324\\right) x^{2} y^{4} + \\left(-18 t^{2} + 324\\right) x^{4} y^{2} - 108 t x^{5} y^{2} + \\left(9 t^{2} - 108\\right) x^{6} + \\left(-8 t^{3} + 108 t\\right) x^{7} - 108 x^{8}$"
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],
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"text/plain": [
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"108*y^6 + (9*t^2 - 324)*x^2*y^4 + (-18*t^2 + 324)*x^4*y^2 + (-108*t)*x^5*y^2 + (9*t^2 - 108)*x^6 + (-8*t^3 + 108*t)*x^7 - 108*x^8"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"ht = Ft.discriminant(z)\n",
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"show(ht)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"id": "8cc358aa-03d1-4b9c-b4ff-87b0324bd55b",
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"metadata": {},
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"outputs": [],
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@ -161,7 +101,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"execution_count": 8,
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"id": "d21a93b0-b0c4-4cd2-b648-f4bca8f78376",
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"metadata": {},
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"outputs": [],
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@ -172,7 +112,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"execution_count": 11,
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"id": "59240908-d672-4520-90e5-7358840f8c23",
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"metadata": {},
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"outputs": [
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@ -182,7 +122,7 @@
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"[(-108) * (-v + u)^3 * (v + u)^3]"
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]
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},
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"execution_count": 8,
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"execution_count": 11,
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"metadata": {},
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"output_type": "execute_result"
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}
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@ -193,7 +133,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"execution_count": 12,
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"id": "a1a4111c-050d-4656-be38-ceac87684b47",
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"metadata": {},
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"outputs": [
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@ -203,7 +143,7 @@
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"[(9) * (v - u)^2 * (v + u)^2 * (12*v^2 + (t^2 - 12)*u^2)]"
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]
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},
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"execution_count": 9,
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"execution_count": 12,
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"metadata": {},
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"output_type": "execute_result"
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}
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@ -214,7 +154,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"execution_count": 13,
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"id": "8ac2847d-121a-4a78-a202-7e1692998c99",
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"metadata": {},
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"outputs": [],
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@ -225,7 +165,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"execution_count": 15,
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"id": "e7884c6b-458b-4d7c-8c8f-376ec4b87c9a",
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"metadata": {},
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"outputs": [
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@ -235,7 +175,7 @@
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"[(108) * v^3 * (v + 2*u)^3, (108) * u^3 * (8*v^3 - u^5)]"
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]
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},
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"execution_count": 11,
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"execution_count": 15,
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"metadata": {},
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"output_type": "execute_result"
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}
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@ -246,7 +186,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"execution_count": 16,
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"id": "442b2c9c-c7f1-4fb9-ac12-bf372d90a342",
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"metadata": {},
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"outputs": [
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@ -257,7 +197,7 @@
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" ((4*t^2)) * u^4 * (9*v^2 + (-2*t)*u^3)]"
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]
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},
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"execution_count": 12,
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"execution_count": 16,
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"metadata": {},
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"output_type": "execute_result"
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}
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@ -320,46 +260,6 @@
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"[p.factor() for p in Ztb.get_polyfaces_dictionary(compact=True) if p.number_of_terms() > 1]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"id": "ea740cbb-5980-45e4-a6c9-695a78324c50",
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"metadata": {},
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"outputs": [],
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"source": [
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"Zt1 = ZetaFunctions(ht1)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"id": "d98d3aec-353c-4dcf-9b8a-1ea5ca93512e",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[((-4*t^2)) * (-9*v^2 + (2*t)*u)]"
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]
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},
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"execution_count": 17,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"ht1 = S(ht(v=v + u)(v=u * v) / u^6)\n",
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"[p.factor() for p in Zt1.get_polyfaces_dictionary(compact=True) if p.number_of_terms() > 1]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "c78e9c40-ee08-4a4b-a0ca-4de12082d245",
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"metadata": {},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "code",
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"execution_count": 24,
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@ -1939,7 +1839,8 @@
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"metadata": {
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"kernelspec": {
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"display_name": "SageMath 10.5.beta3",
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"name": "sagemath-dev"
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"language": "sage",
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"name": "sagemath-devel"
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},
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"language_info": {
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"codemirror_mode": {
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