Expression of type Mult

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.numbers import Add, Exp, Mult, frac, one, subtract, three, two
from proveit.physics.quantum.QPE import _eps

# build up the expression from sub-expressions
sub_expr1 = frac(one, _eps)
expr = Mult(_eps, frac(Mult(Exp(_eps, subtract(two, one)), Add(three, sub_expr1)), Mult(Exp(_eps, two), Exp(Add(two, sub_expr1), 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())

\epsilon \cdot \frac{\epsilon^{2 - 1} \cdot \left(3 + \frac{1}{\epsilon}\right)}{\epsilon^{2} \cdot \left(2 + \frac{1}{\epsilon}\right)^{2}}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 7 operands: 1
1	ExprTuple	32, 2
2	Operation	operator: 29 operands: 3
3	ExprTuple	4, 5
4	Operation	operator: 7 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 16 operands: 13
10	Operation	operator: 22 operands: 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	32, 18
14	ExprTuple	19, 26
15	ExprTuple	32, 25
16	Literal
17	ExprTuple	20, 25
18	Operation	operator: 22 operands: 21
19	Literal
20	Operation	operator: 22 operands: 23
21	ExprTuple	25, 24
22	Literal
23	ExprTuple	25, 26
24	Operation	operator: 27 operand: 31
25	Literal
26	Operation	operator: 29 operands: 30
27	Literal
28	ExprTuple	31
29	Literal
30	ExprTuple	31, 32
31	Literal
32	Literal