Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprTuple, Lambda, l
from proveit.logic import InSet
from proveit.numbers import Exp, Mult, four, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _pos_domain

# build up the expression from sub-expressions
sub_expr1 = Exp(_diff_l_scaled_delta_floor, two)
sub_expr2 = InSet(l, _pos_domain)
expr = ExprTuple(Lambda(l, Conditional(frac(one, Mult(four, sub_expr1)), sub_expr2)), Lambda(l, Conditional(Mult(frac(one, four), frac(one, sub_expr1)), sub_expr2)))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(l \mapsto \left\{\frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \textrm{ if } l \in \{e + 1~\ldotp \ldotp~2^{t - 1}\}\right.., l \mapsto \left\{\frac{1}{4} \cdot \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \textrm{ if } l \in \{e + 1~\ldotp \ldotp~2^{t - 1}\}\right..\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Lambda	parameter: 36 body: 3
2	Lambda	parameter: 36 body: 5
3	Conditional	value: 6 condition: 8
4	ExprTuple	36
5	Conditional	value: 7 condition: 8
6	Operation	operator: 19 operands: 9
7	Operation	operator: 44 operands: 10
8	Operation	operator: 11 operands: 12
9	ExprTuple	43, 13
10	ExprTuple	14, 15
11	Literal
12	ExprTuple	36, 16
13	Operation	operator: 44 operands: 17
14	Operation	operator: 19 operands: 18
15	Operation	operator: 19 operands: 20
16	Operation	operator: 21 operands: 22
17	ExprTuple	23, 24
18	ExprTuple	43, 23
19	Literal
20	ExprTuple	43, 24
21	Literal
22	ExprTuple	25, 26
23	Literal
24	Operation	operator: 48 operands: 27
25	Operation	operator: 34 operands: 28
26	Operation	operator: 48 operands: 29
27	ExprTuple	30, 52
28	ExprTuple	31, 43
29	ExprTuple	52, 32
30	Operation	operator: 34 operands: 33
31	Variable
32	Operation	operator: 34 operands: 35
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	53, 38
36	Variable
37	Operation	operator: 40 operand: 42
38	Operation	operator: 40 operand: 43
39	ExprTuple	42
40	Literal
41	ExprTuple	43
42	Operation	operator: 44 operands: 45
43	Literal
44	Literal
45	ExprTuple	46, 47
46	Operation	operator: 48 operands: 49
47	Operation	operator: 50 operand: 54
48	Literal
49	ExprTuple	52, 53
50	Literal
51	ExprTuple	54
52	Literal
53	Literal
54	Literal