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
from proveit.numbers import Add, Exp, Mult, Neg, four, frac, one, subtract, two
from proveit.physics.quantum.QPE import _eps, _n, _t

# build up the expression from sub-expressions
sub_expr1 = Add(one, frac(one, Mult(two, _eps)))
sub_expr2 = Neg(frac(one, Mult(two, sub_expr1)))
expr = ExprTuple(Add(one, sub_expr2, Neg(frac(one, Mult(four, Exp(sub_expr1, two))))), Add(one, sub_expr2, Neg(frac(one, Mult(four, Exp(subtract(Exp(two, subtract(_t, _n)), one), two))))))

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(1 - \frac{1}{2 \cdot \left(1 + \frac{1}{2 \cdot \epsilon}\right)} - \frac{1}{4 \cdot \left(1 + \frac{1}{2 \cdot \epsilon}\right)^{2}}, 1 - \frac{1}{2 \cdot \left(1 + \frac{1}{2 \cdot \epsilon}\right)} - \frac{1}{4 \cdot \left(2^{t - n} - 1\right)^{2}}\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: 45 operands: 3
2	Operation	operator: 45 operands: 4
3	ExprTuple	42, 6, 5
4	ExprTuple	42, 6, 7
5	Operation	operator: 51 operand: 11
6	Operation	operator: 51 operand: 12
7	Operation	operator: 51 operand: 13
8	ExprTuple	11
9	ExprTuple	12
10	ExprTuple	13
11	Operation	operator: 35 operands: 14
12	Operation	operator: 35 operands: 15
13	Operation	operator: 35 operands: 16
14	ExprTuple	42, 17
15	ExprTuple	42, 18
16	ExprTuple	42, 19
17	Operation	operator: 43 operands: 20
18	Operation	operator: 43 operands: 21
19	Operation	operator: 43 operands: 22
20	ExprTuple	24, 23
21	ExprTuple	47, 28
22	ExprTuple	24, 25
23	Operation	operator: 37 operands: 26
24	Literal
25	Operation	operator: 37 operands: 27
26	ExprTuple	28, 47
27	ExprTuple	29, 47
28	Operation	operator: 45 operands: 30
29	Operation	operator: 45 operands: 31
30	ExprTuple	42, 32
31	ExprTuple	33, 34
32	Operation	operator: 35 operands: 36
33	Operation	operator: 37 operands: 38
34	Operation	operator: 51 operand: 42
35	Literal
36	ExprTuple	42, 40
37	Literal
38	ExprTuple	47, 41
39	ExprTuple	42
40	Operation	operator: 43 operands: 44
41	Operation	operator: 45 operands: 46
42	Literal
43	Literal
44	ExprTuple	47, 48
45	Literal
46	ExprTuple	49, 50
47	Literal
48	Literal
49	Literal
50	Operation	operator: 51 operand: 53
51	Literal
52	ExprTuple	53
53	Literal