diff --git a/DeformacionGenerica0.ipynb b/DeformacionGenerica_0.ipynb similarity index 97% rename from DeformacionGenerica0.ipynb rename to DeformacionGenerica_0.ipynb index 5123f8b..b192593 100644 --- a/DeformacionGenerica0.ipynb +++ b/DeformacionGenerica_0.ipynb @@ -5,7 +5,23 @@ "execution_count": 1, "id": "72d5a30c-1a59-4a55-9680-fdfa7979625b", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "\\(\\displaystyle z^{3} - 3 y^{2} z + 3 x^{2} z + 2 x^{4}\\)" + ], + "text/latex": [ + "$\\displaystyle z^{3} - 3 y^{2} z + 3 x^{2} z + 2 x^{4}$" + ], + "text/plain": [ + "z^3 - 3*y^2*z + 3*x^2*z + 2*x^4" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# load('zetas_triples_general.py')\n", "R. = PolynomialRing(QQ, order='neglex')\n", @@ -13,7 +29,8 @@ "f = v^2 - u^2\n", "g = u^4\n", "F = z^3 - 3 * f(u=x, v=y) * z + 2 * g(u=x, v=y)\n", - "h = F.discriminant(z)(x=u, y=v)" + "h = F.discriminant(z)(x=u, y=v)\n", + "show(F)" ] }, { @@ -72,6 +89,21 @@ "id": "27e92ddc-34d6-4290-880f-9d3561a8ec4e", "metadata": {}, "outputs": [ + { + "data": { + "text/html": [ + "\\(\\displaystyle z^{3} - 3 y^{2} z + t x z^{2} + 3 x^{2} z + 2 x^{4}\\)" + ], + "text/latex": [ + "$\\displaystyle z^{3} - 3 y^{2} z + t x z^{2} + 3 x^{2} z + 2 x^{4}$" + ], + "text/plain": [ + "z^3 - 3*y^2*z + t*x*z^2 + 3*x^2*z + 2*x^4" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, { "data": { "text/plain": [ @@ -85,12 +117,40 @@ ], "source": [ "Ft = F + t * x * z^2\n", + "show(Ft)\n", "Ft.jacobian_ideal().vector_space_dimension()" ] }, { "cell_type": "code", "execution_count": 5, + "id": "83328b3a-8da8-4adc-8b6c-02764b1420d3", + "metadata": {}, + "outputs": [ + { + "data": { + "text/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}\\)" + ], + "text/latex": [ + "$\\displaystyle 108 y^{6} + \\left(9 t^{2} - 324\\right) x^{2} y^{4} + \\left(-18 t^{2} + 324\\right) x^{4} y^{2} - 108 t x^{5} y^{2} + \\left(9 t^{2} - 108\\right) x^{6} + \\left(-8 t^{3} + 108 t\\right) x^{7} - 108 x^{8}$" + ], + "text/plain": [ + "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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ht = Ft.discriminant(z)\n", + "show(ht)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, "id": "8cc358aa-03d1-4b9c-b4ff-87b0324bd55b", "metadata": {}, "outputs": [], @@ -101,7 +161,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 7, "id": "d21a93b0-b0c4-4cd2-b648-f4bca8f78376", "metadata": {}, "outputs": [], @@ -112,7 +172,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 8, "id": "59240908-d672-4520-90e5-7358840f8c23", "metadata": {}, "outputs": [ @@ -122,7 +182,7 @@ "[(-108) * (-v + u)^3 * (v + u)^3]" ] }, - "execution_count": 11, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -133,7 +193,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 9, "id": "a1a4111c-050d-4656-be38-ceac87684b47", "metadata": {}, "outputs": [ @@ -143,7 +203,7 @@ "[(9) * (v - u)^2 * (v + u)^2 * (12*v^2 + (t^2 - 12)*u^2)]" ] }, - "execution_count": 12, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } @@ -154,7 +214,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 10, "id": "8ac2847d-121a-4a78-a202-7e1692998c99", "metadata": {}, "outputs": [], @@ -165,7 +225,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 11, "id": "e7884c6b-458b-4d7c-8c8f-376ec4b87c9a", "metadata": {}, "outputs": [ @@ -175,7 +235,7 @@ "[(108) * v^3 * (v + 2*u)^3, (108) * u^3 * (8*v^3 - u^5)]" ] }, - "execution_count": 15, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } @@ -186,7 +246,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 12, "id": "442b2c9c-c7f1-4fb9-ac12-bf372d90a342", "metadata": {}, "outputs": [ @@ -197,7 +257,7 @@ " ((4*t^2)) * u^4 * (9*v^2 + (-2*t)*u^3)]" ] }, - "execution_count": 16, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" } @@ -260,6 +320,46 @@ "[p.factor() for p in Ztb.get_polyfaces_dictionary(compact=True) if p.number_of_terms() > 1]" ] }, + { + "cell_type": "code", + "execution_count": 16, + "id": "ea740cbb-5980-45e4-a6c9-695a78324c50", + "metadata": {}, + "outputs": [], + "source": [ + "Zt1 = ZetaFunctions(ht1)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "d98d3aec-353c-4dcf-9b8a-1ea5ca93512e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[((-4*t^2)) * (-9*v^2 + (2*t)*u)]" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ht1 = S(ht(v=v + u)(v=u * v) / u^6)\n", + "[p.factor() for p in Zt1.get_polyfaces_dictionary(compact=True) if p.number_of_terms() > 1]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c78e9c40-ee08-4a4b-a0ca-4de12082d245", + "metadata": {}, + "outputs": [], + "source": [] + }, { "cell_type": "code", "execution_count": 24, @@ -1838,9 +1938,9 @@ ], "metadata": { "kernelspec": { - "display_name": "SageMath 10.4.rc3", + "display_name": "SageMath 10.5.beta2", "language": "sage", - "name": "sagemath-devel" + "name": "sagemath-dev" }, "language_info": { "codemirror_mode": { @@ -1852,7 +1952,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.12.4" + "version": "3.12.5" } }, "nbformat": 4,