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 ExprTuple, l
from proveit.numbers import Abs, Exp, Mult, Neg, four, frac, one, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _t, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Exp(two, Neg(_t))
sub_expr2 = Abs(subtract(_delta_b_floor, Mult(l, sub_expr1)))
expr = ExprTuple(frac(two, Mult(four, _two_pow_t, sub_expr2)), Mult(frac(one, two), sub_expr1, Exp(sub_expr2, Neg(one))))

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(\frac{2}{4 \cdot 2^{t} \cdot \left|\delta_{b_{\textit{f}}} - \left(l \cdot 2^{-t}\right)\right|}, \frac{1}{2} \cdot 2^{-t} \cdot \left|\delta_{b_{\textit{f}}} - \left(l \cdot 2^{-t}\right)\right|^{-1}\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	Operation	operator: 9 operands: 3
2	Operation	operator: 31 operands: 4
3	ExprTuple	37, 5
4	ExprTuple	6, 34, 7
5	Operation	operator: 31 operands: 8
6	Operation	operator: 9 operands: 10
7	Operation	operator: 35 operands: 11
8	ExprTuple	12, 13, 14
9	Literal
10	ExprTuple	21, 37
11	ExprTuple	14, 15
12	Literal
13	Operation	operator: 35 operands: 16
14	Operation	operator: 17 operand: 20
15	Operation	operator: 39 operand: 21
16	ExprTuple	37, 41
17	Literal
18	ExprTuple	20
19	ExprTuple	21
20	Operation	operator: 22 operands: 23
21	Literal
22	Literal
23	ExprTuple	24, 25
24	Operation	operator: 26 operand: 29
25	Operation	operator: 39 operand: 30
26	Literal
27	ExprTuple	29
28	ExprTuple	30
29	Literal
30	Operation	operator: 31 operands: 32
31	Literal
32	ExprTuple	33, 34
33	Variable
34	Operation	operator: 35 operands: 36
35	Literal
36	ExprTuple	37, 38
37	Literal
38	Operation	operator: 39 operand: 41
39	Literal
40	ExprTuple	41
41	Literal