Main functions

main_v111_higher53_multicore_parallel.sage

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Functions

Function name	Purpose
immutabilize	Immutabilizes mutable Sage objects such as matrices, so that sets of such Sage objects can be formed.
duplikiller	Used to remove duplicates from a list, in the simplest possible way, with a for loop.
hamster1	Used to remove duplicates from a list, using OrderedDict. That is, takes a list input_list as input, and returns list(OrderedDict.fromkeys(input_list)) Faster than duplikiller when huge lists are involved.
ChunkMaster	Takes a list seq and an integer num as input. Splits fairly the list seq into a number num of chunks. Mobilized at the beginning of each iteration of Borcherds’ method when the PFB / APFB parallel approach is used.
ALG	Used to execute our implementation ShiVectors of Shimada’s SLVE within DEFINING_SET.
TRIPLER	Used in DEFINING_SET to form a suitable triple that can be used as input data into ALG when the latter is executed within DEFINING_SET. The function TRIPLER forms the triple highlighted in yellow on this screenshot of page 90 of our thesis.
ISOLATOR	Used by TRIPLER to compute the column vector made of inner products in $S^{\vee }$, highlighted in orange on this screenshot of page 90 of our thesis.
PR_TRIPLE	Used to compute the projection of a positive quadratic triple $QT$. Take a look at the expression of $$\mathbf{\text{pr}}(QT)$$ on page 74 of the thesis for more details.
IOTA_STAR	Takes an integer $a$ and a triple $QT$ as input. Returns $${\iota }^{\ast }(a,QT).$$ See expression (1.10), section 1.4 of the thesis, p74, for more details.
TRIPLES_BUILDER	From the input data of a triple $QT$, the function TRIPLES_BUILDER is used to compute the set $\mathcal{S}(QT)$ of triples mentioned at the beginning of section 1.4.1 page 75 of our thesis.
q_QT	From the input data of a triple $QT$, the function q_QT outputs the expression $$q_{QT}(\mathbf{\text{x}})$$ mentioned at the beginning of page 73 of our thesis.
SOLVER	Used to compute the solution set $\mathcal{X}(\mathcal{S}(QT))$ of the inequality $q_{QT}(\mathbf{\text{x}})\le 0$ where $QT$ is the triple of a single variable contained in $\mathcal{S}(QT)$. See page 76 of our thesis for more details.
ALGO	This function is an implementation of the main routine behind the procedure ShiVector, mentioned in the thesis, Section 1.4.1 – page 76.
sum2
SOL_GEN
DEFINING_SET
run_multicore_op
multi_op_2
SPAN_CHECK_OLD
multi_op_3
multi_op_sol_gen
SPAN_CHECK
DELTA_W
DELTA_W_TRUE
DELTA_W2
AC_Finder
quotest
reflector
ORTHIZER
multi_SetOfWalls_op
DSD_COMPUTER2_OLD
DSD_COMPUTER2
AUT_CHAMBER
hamster1
ORB_FINDER
ORB_TESTER_IS_CONTAINED
CONG_CHECKER_CUSTOM	Takes the set of walls of a ${\mathcal{P}}_S$-chamber $\mathrm{\Omega }(D_1)$ , the set of walls of a ${\mathcal{P}}_S$-chamber $\mathrm{\Omega }(D_2)$ and the Weyl vector of $D_2$. Determines whether $D_1$ and $D_2$ are $\mathbf{H}$-congruent.
multi_op_4
multi_op_5
rat_detector
rat_detector_alt	NOT USED IN OUR IMPLEMENTATION OF BM Takes an element of $m\in S^{\vee }$ expressed with respect to the basis ${\mathcal{B}}_1$ for $S^{\vee }$ and determines whether $m$ is a $(-2)-wall.
RAT_DETECT	NOT USED IN OUR IMPLEMENTATION OF BM Takes a Weyl vector of a chamber as input. Displays the set of walls of the chambers and indicates whether such or such wall is a $(-2)$-wall.
G_simplifier	Takes as input a list of matrix transformations and processes the list in such a way that the list $\mathcal{L}$ obtained as output is such that $$\text{Id}\notin \mathcal{L}\text{and}g\in \mathcal{L}\Rightarrow g^{-1}\notin L$$