ore_algebra.examples.periods

Periods of hypersurfaces

This file contains examples of Picard-Fuchs equations taken from Emre Sertöz’ periods-suite (see <URL: https://github.com/period-suite >).

See the large_examples package for many larger equations of the same type, also provided by Emre Sertöz.

Reference: Emre Can Sertöz, Computing Periods of Hypersurfaces, arXiv:ZZ(1803).ZZ(08068) [math.AG], ZZ(2018).

TESTS:

sage: from ore_algebra.examples.periods import allODEs

sage: allODEs[0][17].numerical_transition_matrix([0,1], assume_analytic=True)
[ [0.9902279797337334...]  [0.9785547044657048...]]
[[-0.0381995909776051...]   [2.852042263413222...]]

sage: allODEs[1][17].numerical_transition_matrix([0,1], assume_analytic=True)
[ [0.4436008055581744...]  [0.2576912112960792...] [0.08363620203452759...]  [0.2016411824751549...]]
[[-0.5578441859228735...] [-0.2358519460794672...] [-0.1779340731492937...]  [0.0274665947131637...]]
[ [0.6254187045596549...]  [0.2501374981058974...]  [0.1609650808189804...] [-0.2230856229812542...]]
[[-0.4162345564115225...] [-0.1109458334615996...]  [0.0531985258846558...]  [0.3359776326651218...]]

sage: allODEs[2][0].numerical_transition_matrix([0,1], assume_analytic=True)
[  [1.004115547920436...]  [0.9250482975429899...]   [1.361476133724963...]  [0.3062894779173804...]   [1.938640071541597...]]
[[0.02081552213646102...]  [0.6270570933062987...]   [3.810301366251934...] [-0.3577127637793245...]   [8.513753305220071...]]
[[0.04188669311383054...] [-0.7342371576863916...]   [4.610035363931867...]  [-3.333166426230457...]   [14.56296824974653...]]
[[0.04198148492753871...] [-0.7149264076935399...]   [3.612663748781155...]  [-4.700677038444421...]   [12.15139319879300...]]
[[0.02222358650439156...] [-0.3691184858549074...]   [1.978544499665723...]  [-2.464594622238230...]   [5.583417676436902...]]

sage: from ore_algebra.examples.periods import dop_140118_4, dop_140118_6_4_2
sage: dop_140118_4.numerical_transition_matrix([0,1], 1e-200, assume_analytic=True, squash_intervals=True)[0,0] # long time (3.4 s)
[0.715789877802957863238550457253731250968474707759494604384565678079788875083797614717578209783780445614354477440408242665736695668023525540188926510250252867846105078425273565096207343428573617619055...]

sage: dop_140118_6_4_2.numerical_transition_matrix([0,0.6+0.2*I,1], 1e-150, assume_analytic=True)[0,0] # long time (46 s)
[0.869416096203083843226211954657998870957512910057684233369962964198185589472701159476011286381945095930579858841819223890538...] +
[0.111837076188766007428795107583040967018817636196931759352101655227626469869765071421524590125612423060982791983438726224032...]*I